Apologies for the poor English, hope the question is still understandable
The Battle of the Huertgen Forest was a serious mistake (the extent of the true scale of the disaster remained classified until the 1950's and it is still poorly understood today) on the part of the Americans during WWII. It lasted six months from September 1944 until February 1945 and cost about 33,000 American casualties. It potentially delayed the end of World War II in Europe by months, as the Americans were unable to break through the Westwall by the time winter hit and were forced to dig in and wait until the spring thaw (March 1945) to launch any sort of offensive into the heart of Germany.
The Americans attacked blindly into the forest dozens of times without their usual advantages of armor and air support, and paid dearly for it. Ten American divisions and a Ranger battalion were chewed up and spat out by a combination of poor weather and terrain, halfhearted planning, and a vicious, well-executed German defense. Courtney Hodges told in an interview in 1983 that he
"would never pick it (the forest) as the place to be. it was assigned as part of my corps sector, and reluctantly we had to fight in it..."
The implied objective within the forest, the important series of Roer River dams, was not even defined as one until late in November 1944 when Courtney Hodges pushed for air attacks (which never happened) on the dams to prevent their usage as a weapon by the Germans to delay the allied advance.
If the Americans had not attacked into the heart of the forest, but had instead swung south, around it, and attacked the dams from the side and behind, the battle could have been won by late October or early November, offering American ground units a firm foothold in Germany and a chance to dig in before winter arrived.
Sources:
The Battle of the Huertgen Forest - Scorpio's Website http://home.scarlet.be/~sh446368/home.html
Miller, Edward G. A Dark and Bloody Ground: The Huertgen Forest and the Roer River Dams, 1944-1945. N.p.: Texas A&M UP, 1995. Print.
United States Army in World War II, European Theater of Operations: The Siegfried Line Campaign http://www.ibiblio.org/hyperwar/USA/USA-E-Siegfried/index.html
Most of the responses seem to be about tactical issues on the Western front with losses of a few thousand men. It's not even clear that these are obvious errors.
The Eastern Front (where 30 million died), which was the decisive main reason for the defeat of Germany, seems to have been completely overlooked.
Where Stalin purged the Soviet army before Barbarossa; and ignored intelligence to leave the army unprepared for Barbarossa, where during Barbarossa itself entire Soviet armies were surrounded and destroyed (often with 'not one step back' ringing in their ears), where the Russians fought a bitter war with Finland for marginal land gains, where winter offensives initially made only moderate gains and summer battles were costly and often (at least initially) led to not very great results.
If I were to look for Allied mistakes that extended the war, it would be the Eastern Front I would examine for strategic errors. Not minor skirmishes and tactical battles late on the western front.
And how is it that no one has mentioned the misplaced French reliance on the Maginot line early on ?
The evidence of the posts so far shows the casual reader predominantly focusing on british and us efforts late in the war and it seems to me that this is a misplaced focus.
/u/the_howling_cow actually linked the same thing I was going to, but the first half of United States Army in World War II, European Theater of Operations: The Siegfried Line Campaign, mentions Operation Market Garden, which is often mentioned as an operation that set them back to a longer conflict.
The Allies failed to cross the Rhine in sufficient force and failed to hold the bridges and locations they sought and wouldn't break through until March 1945 - in fact, Arnhem itself would not be liberated until mid April of 1945.
It also changed a lot of military thinking to this day, regarding the employment of lightly armed paratroopers with little support, especially those being dropped into areas where the potential of engaging heavy enemy units
In the Pacific Theatre, a critical mistake was cost-cutting in the U.S. submarine force that led to an inadequate testing program for its Mark 14 torpedo and the Mark 6 magnetic influence exploder within.
These testing flaws ensured that when the war broke out, U.S. submarines (except those armed with WWI-era torpedoes) had an abysmal record of success.
Only after the problems were discovered and repaired by 1943 did American submarines come into their own, almost entirely destroying the Japanese merchant marine and greatly hampering Japanese naval operations.
The problems with the Mark 14 would have been discovered easily in a normal testing program, but Depression-era cost cutting meant tests of the production model were curtailed or didn't happen at all. Had the Mark 14 been fully capable in December 1941, the Japanese merchant marine would have found itself in its 1945 position by 1943, as early war Japanese antisubmarine techniques and equipment was extraordinarily primitive.
The Battle of Anzio comes to mind. It started in January of 1944 and ended in June of 1944. It took so long because it was a stalemate for a very torturous few months. The allies lost 7,000 men and also had about 36,000 missing or wounded and another 44,000 non-battle injuries. German casualties were similar. Some say that the operation did tie up a few German divisions in Italy when Operation Overlord (the Normandy landings) happened a few days after the Anzio campaign ended, but others argue that the Ally resources could have gone elsewhere and the campaign could have reached Rome much earlier if better planned.
Here's some books to read on this: Anzio: Italy and the Battle for Rome - 1944 by Lloyd Clark. They Fought At Enzio by John Eisenhower. Here's a little pamphlet that gives a nice little chronology of the battle.
It's easier to tie decisions late in the war to prolonging it, while mistakes early in the war are further back the chain of events, and more difficult tie directly to shortening the war, but they clearly were undeniable early mistakes.
The first is the phoney war (a.k.a. the sitzkrieg). In spite of the tropes on reddit, France really did have a well equipped modern army. The allies (France and UK) missed the chance to plan a defense in depth, or possibly do more than just the Saar offensive, something to actually pull some heat off of Poland.
A second early mistake has to be the failure to set up convoys along the east coast of the U.S. and a "happy time" for the U boats. Over 600 ships sunk makes for a senseless loss of lives and material there.
It's hard to put a number on how much these prolonged the war, and the course of the war could have turned out entirely different. Maybe if France held out longer, it would have turned into a repeat of WW1 and then the story becomes even more speculative.
The fall of Singapore is probably a biggie and I'm surprised that nobody mentioned it. There were a number of issues on the Allied side, from inexperienced command putting soldiers in the wrong places to the attempt to defend the island with armour-piercing shells, which work well against battleships, but are hopeless against infantry marching over soft, muddy ground (most of the time, they didn't even detonate).
The Japanese were at the end of their supply lines with less than a day of munitions when it was surrendered. Without the loss of Singapore (or at least a more orderly withdrawal), massive numbers of Allied troops were lost and many killed. Also, the Japanese convinced a number of Indian soldiers that were captured in Singapore to fight for them and eventually against the British in Burma.
Sources:
The management of the SOE was hopelessly mucked up, with superiors ignoring very obvious indications that some agents had been compromised and delivering both supplies and agents right into the hands of the Germans. This resulted in the deaths of SOE agents and members of the French resistance, as well as depriving the resistance of needed materials.
As an example, radio operators were supposed to transmit one code which supposedly confirmed that they were operating freely, and then transmit another code which actually indicated that they were free. When radio operators failed to use the second code, they were informed that they'd forgotten to use it and reminded to use it next time (which of course meant the captured SOE operators were then known to be non-cooperative, and the Germans knew how to correctly falsify information). Instead of drawing the obvious conclusion that the agents were in enemy hands, decisions were made on the assumption that they were not.
The book 'A Life in Secrets: The Story of Vera Atkins and the Lost Agents of SOE' by Sarah Helm focuses more on post-war uncovering of what happened to the captured SOE agents but does not mince words when it comes to describing just how badly the operation was run.
The biggest mistakes for the Allies came at the beginning of the war. From hindsight it tends to look like all preamble for the war that was about to come. But the war didn't start like you would set up a game of Axis and Allies. While blitzkreig attacks were able to knock out countries in quick succession, that doesn't imply that those countries were always going to be taken by Axis powers. Battles and campaigns could have gone differently. Defences and forces could have been better prepared or allocated. Either of which would have made a huge difference in the progress of the war.
Take the Fall of France. This is probably the biggest loss during the initial part of the war. Not only was an important ally basically wiped out, it gave Germany air bases to attack England and naval bases to attack Atlantic shipping. This was a major mistake of allied planning and execution that could have gone very differently with a little better vision or leadership.
Beyond that there were a number of other territorial losses like France, but to a smaller extent. Norway. Greece. The Philippines. Singapore. (I would say Poland, but they have a rough history of being gobbled up by larger neighbors. I don't see a way they could fend off attacks from Germany and the Soviet Union at the same time.)
It isn't that the Allies didn't make mistakes later in the war, but they were no longer making the huge strategic mistakes. The Axis powers on the other hand started getting more desperate and making bigger blunders. Those get remembered as huge disasters, where the early Allied losses seem to be forgotten.
The 1942 Dieppe Raid is arguably the greatest disaster in Canadian military history, though its failures were considered when the D-Day invasion was planned two years later.
From a British perspective, failing to exploit the success of Operation Compass.
Following their declaration of war in September 1940, the Italian army in Libya attacked British held Egypt. They advanced about 70 miles but were not engaged to any significant degree by the numerically inferior Western Desert Force under Lt Gen Richard O'Connor. In December 1940 the British launched a counter-offensive, Operation Compass, which was wildly successful. In what began as merely a 5 day raid on Italian positions, O'Connor's 30,000 men sent Marshall Graziani's 150,000 strong 10th Army into headlong retreat. 138,000 Italians were captured. The operation continued and O'Connor advanced over 800 miles in two months, taking Benghazi.
The advance was halted when Axis forces invaded Greece in April 1941, and British high command diverted the core of O'Connor's force to Greece, in what would ultimately be a fruitless defence of Greece and later Crete. It has been argued that with sufficient resources, O'Connor could have captured Tripoli and have put up a much stiffer defence against Rommel (who ultimately retook all the territory taken by the British), and therefore have shortened the Western Desert Campaign.