There was a lot of inter-allies bickering, particularly between the US and Brits. One of the more well-known examples was Mark Clark and the capture of Rome. (Most of my knowledge is from Rick Atkinson's 'The Day of Battle'.) Clark wanted to be the general who took Rome. After a long slog that included Cassino and the landings and Anzio, the Allies were able to break out and head for Rome from the south. Clark was worried that Alexander (the overall commander of forces in Italy) was going to let the British get to Rome before him. Clark carried out his orders to cut roads to Rome but took a large portion of his force and sent them to Rome.
There was a feeling amongst the US Army that the British were manipulating the US forces and taking most of the glory for themselves. FDR was also concerned that British war planning was concerned with retaining the British empire. The coalition was at risk of fracturing at any time. Maintaining the alliance was without a doubt Eisenhower's greatest accomplishment.
eta - I'm 1/2 way thru Atkinson's 3rd book of the European War (Army at Dawn, Day of Battle, and Guns at Last Light) and he does an excellent job of discussing the squabbles between British and US forces at all levels of command.
In his Band of Brothers, Stephen Ambrose describes how the U.S. 101st Airborne Division was in a race against the French 2d Armored Division to reach Berchtesgaden. Overall, this was part of a plan to prevent a guerrilla warfare-esque holdout in southern Germany/Austria/the Alps, but realistically the capture of Berchtesgaden was more of a prestigious goal than a strategic one. Ambrose describes how Easy Company was the first unit to reach the area. Commence partying
However, the 1st battalion of the 7th Regiment of the the 3d Infantry Division actually got there first, about a day ahead of the 101st. The 3d Infantry Division had been tasked with capturing Salzburg, and after encountering no resistance, was in the unexpected position of being the nearest unit to Berchtesgaden. They were not ordered to do so, but the 3d Infantry's CO, Major General O'Daniel, made the decision to send Colonel Heintges' 1st battalion forward. L Company also arrived soon after.
In fact, 3d Infantry reportedly held the only two bridges over the Saalach River, and upon the arrival of the French forces, O'Daniel refused passage across the bridges. Eventually the French did get across and into Berchtesgaden; the 101st arrived the following day and assumed the role of occupation.
Related article, with more details: http://www.historynet.com/world-war-ii-race-to-seize-berchtesgaden.htm
One of the major reason for Bradley's disdain for Patton was this hunt for glory mentality even if it meant more casualties than necessary. For example; "patton wanted to present Metz to Marshall as a trophy during his impending visit to the Third Army... 'if it took every man in XX Corps', saying it could not permit a third Army attack to fail.
But fail it did."
This from D'este's biography, not an apologist but surely one of Patton's greatest supporter's.
As casualties mounted Patton continued the attack "with justification of 'blooding' new divisions..."
So this competition for recognition and glory surely cost lives
I garnered some insight into this from the book Twelve Desperate Miles, about the SS Contessa, a banana boat that was drafted into the USA's initial charge into North Africa, author Tim Brady spends some time discussing why the USA was going into North Africa in the first place, rather than a direct charge into Europe, and disagreement with Britain about how the war would be waged was a big part of that reason.
On top of that, the book describes in detail the initial Vichy France military members who were defeated. There was some doubt as to whether or not the military would remain loyal to Vichy France, or if they would choose to fight. It seems there was good reason for doubt, as the captured military forces themselves were split; some choosing to continue to fight, others choosing to switch sides.
The phrase "unnecessary costs" that you use assumes a certain point of view, that all of the Allies had the exact same goals when, as always has been and always shall be, they each had different goals, things they wanted from the defeat of Germany, and old rivalries to boot. Prior to WW2, Americans saw the English as stuffy and foppish; however, during the war, American correspondents reporting from England as the Blitz happened (see also Cronkite's War exposed Americans to an entirely different side of the English, the stout-hearted, "stiff-upper-lip during rough times" image.
This isn't a direct answer, but you may be interested in The Liberation Trilogy by Rich Atkinson. One of the most interesting things he talks about is the shift of political power between Great Britain and the United States over the course of the war. It covers an extraordinary amount of stories around competition between the US and UK, but also with Soviet Russia and even between the Axis.
As an example, one of the last major inputs that the English were able to win over was the focus of the United States on a "Europe First" policy. It symbolizes the shift between major powers and indeed the relationship between western nations that would happen well after the war.