I understand that this is probably an issue of dispute and am more interested in knowing the range of opinions than "the answer." I have heard it thrown about that the worst/most decisive error made by Germany during WWII (save probably the invasion of Russia) was the decision to stop attacking RAF airfields and begin bombing London in an ultimately futile effort to destroy British morale. I have also heard that, to the contrary, the airfield bombing was also unlikely to ultimately succeed given the RAF's inherent advantages as the defending air force and so the error was minor or irrelevant. My instinct is to lean against the more dramatic reading since people have an incentive to punch up the importance of individual crux moments for dramatic purposes, but I'm curious to hear informed opinions on the issue.
Excellent question, and one that will probably generate a lot of debate. You mentioned yourself that there are multiple arguments that support each conclusion, and I offer you this [thread] (http://www.reddit.com/r/AskHistorians/comments/1glsou/why_did_the_germans_lost_the_battle_of_britain/) from 9 months ago that discussed this exact topic as a kind of overview.
I support the theory that it was a decisive error. Operation Sea Lion was an intricately planned tour de force by the Wehrmacht, Luftwaffe, and Kriegsmarine that had the ultimate goal of invading Britain. The first phase of this plan was the establishment of absolute sea and air power for the German military machine, so it could support a land invasion.
That's all well and good, but look at how many factors take part in the invasion. The British are defending home turf, there's only a brief 5-6 month window in which an invasion is possible (is this starting to sound like [another invasion] (http://en.wikipedia.org/wiki/Operation_Barbarossa) that the German military launched itself into...?) and the British have fighter command and a militarized civilian defense force, along with a powerful Navy, in which to fight off the Germans. So it's going to turn into a brawl, and one in which the Western forces have been preparing for since before the war. So Hitler approached Goering with the objective that he must bomb the RAF into oblivion by destroying their squadrons on the ground (a tactic that has remained relatively unchanged until the modern era of warfare) and Goering sets out to do just that. The only problem is, Goering and his Luftwaffe do not have the necessary tools to complete this objective. This is a result of the German tactics of Blitzkrieg that were developed during the interwar periods and used extensively at the onset of the war. According to Blitzkrieg doctrine, the name of the game is fast, decisive movements that are aimed at the schwerpunkt (centerpoint) of the battlefield, i.e. the front lines. The purpose of this is to overwhelm and confuse the enemy, which the Wehrmacht can overrun and subsequently penetrate deep into enemy territory. This is entirely different than the strategic, tactical long term bombing objective that Goering must carry out. Thus, his bomber force, which consists of 2-3 engine medium bombers such as the Heinkel He-111, Junkers Ju-87 and the Dornier Do-17, is poorly suited for the job. These types of bombers, termed schnellbombers by the Germans, were a kind of middle ground between a lumbering heavy bomber and a fighter bomber that could defend itself in the event of an aerial attack. In reality, they weren't very good at either role. They were too slow to outrun fighter aircraft, lacked the armaments to defend itself in a dogfight, and lacked the bomb carrying capability to effectively level the target.
This caused disproportionately high losses among Luftwaffe bomber squadrons during the Battle of Britain, and also resulted in only medium damage to British airfields when the Luftwaffe bombers actually succeeded in breaking through. Also, Luftwaffe fighters like the famed Bf-109 were constantly having to develop new tactics to protect their bombers from their new, untested role. This served the dual purpose of causing high losses of Luftwaffe fighters (losses due to trial by error) and prolonging the lifetime of the RAF (Luftwaffe fighters could not afford to leave the bombers to find targets of opportunity, allowing stricken RAF fighters the ability to get away and fight another day.)
You are correct when you say that sometimes historians like to dramatize crux moments; i've read some accounts that say "the Battle of Britain could have been won if only the Luftwaffe had bombed the airfields for another 3,4,5...x number of weeks." Whether or not the outcome would have been that concrete is up for conjecture; however, i'm of the belief that the RAF would have eventually folded if Goering had stuck to his guns. Unfortunately for the Germans, the Battle of Britain was a war of attrition that Hitler neither had the patience nor the strategy to win. However, it was a war of attrition nonetheless, and RAF pilots would have eventually been worn down to the point of exhaustion or killed outright. This drastically changed when on August 25th, 1940, the Ruhleben bombing raid, carried out by RAF Hampden bombers stationed in Norfolk, England, brought the full wrath of Hitler. This is when, ironically, the Battle of Britain turned into the British favor. With terror bombing and the Blitz now the name of the game, the RAF pilots got a much needed break from the day to day raids on their airfields, and their squadrons could begin to rest, repair, and regroup in order to deal with the new Luftwaffe tactics.
Elsewhere in this thread, /u/IrishWaterPolo asserts the following:
Unfortunately for the Germans, the Battle of Britain was a war of attrition that Hitler neither had the patience nor the strategy to win. However, it was a war of attrition nonetheless, and RAF pilots would have eventually been worn down to the point of exhaustion or killed outright
This, I think, is the source of why I respectfully disagree with their assessment. That was the dominant narrative at the time and in many histories following the war. The RAF was pushed to the brink by the might of the Luftwaffe, and only the daring of RAF pilots and blunders by Hitler kept the British in the war. I no longer find that narrative compelling, for the two below reasons.
Estimates
Consistently, the Germans underestimated the British in terms of planes available and production of replacement aircraft. On the other hand, the British overestimated German fighter strength and production. As a result, the Germans always thought they were quite close to a victory, and the British thought they were just barely hanging on. It's true that the Germans started with more planes, and that the battle was always going to be a battle of attrition. However, German production of aircraft never matched British production. This website is admittedly poorly sourced, but it gives the below table of aircraft production which I cannot find on a moment's notice from my other sources.
Month/British/German
June 446 164
July 496 220
August 476 173
September 467 218
October 469 200
Total 2354 975
A better source is Max Hastings, Inferno.
Through August the Luftwaffe progressively increased the intensity of its assaults, attacking Fighter Command Airfields--though only briefly radar stations. Air Chief Marshal Sir Hugh Dowding, C-in-C of Fighter Command, began the battle with an average of 600 aircraft available for action, while the Germans deployed a daily average of around 750 serviceable bombers, 250 dive-bombers, and over 600 single-engined and 150 twin-engined fighters, organized in three air fleets. Souteast England was the main battleground, but Dowding was also obliged to defend the northeast and southwest from long-range attacks. (Pg 85)
Both air forces wildly overestimated the damage they inflected on each other. But the Germans’ intelligence failure was far more serious, because it sustained their delusion that they were winning. Fighter Command’s stations were targeted by forty Luftwaffe raids during August and early September, yet only two—Manston and Lympne on the Kent coast—were put out of action for more than a few hours, and the radar recievers were largely spared from attention. By late August the Luftwaffe believed Fighter Command’s first-line strength had been halved, to 300 aircraft. In reality, however, Dowding still deployed around twice that number: attrition was working to the advantage of the British. Between 8 and 23 August, the RAF lost 204 aircraft, but during that month 476 new fighters were built, and many more repaired. The Luftwaffe lost 397, of which 181 were fighters, while only 313 Bf-109s and Bf-110s were produced by German factories. Fighter Command lost 104 pilots killed in the middle fortnight of August, against 623 Luftwafffe airmen dead or captured. (Pg 85-86, emphasis mine)
This source gives another statistic that bolsters the argument that the RAF was winning the battle of attrition.
The war of attrition took its toll from July 1940 to the end of the battle in early October. German fighter strength fell from 725 to 275. With production outpacing losses, RAF fighter planes rose from 644 to 732.
The Battle of Britain was a battle of attrition, but it was being won by the British.
British options
Many narratives make an assumption that is unwarranted—the British had to continue their defense as they began it. This is simply not true. At any point, the British could have moved their fighter bases further north—out of the reach of the Germans’ ability to make escorted attacks. The RAF was hard pressed in the Battle of Britain, but had they needed a breather—and it turns out the Germans needed one far worse—they could have relocated their bases to the north and played for time. So long as the RAF was not defeated, an invasion of Britain was going to be incredibly difficult. The British chose to defend as far forward as they could so that they could do as much damage as possible to the Luftwaffe and so they could try to spare some of their island from harm. A more northerly defense would have meant more damage to British cities and less damage to the Luftwaffe, but it would have also preserved the RAF from being hurt on the ground.
My conclusions
In my opinion, the German error in the Battle of Britain was attacking an enemy that they had no way of knocking out of the war and who had greater aircraft production. (Edit) At no point during WWII did Germany outproduce the UK in aircraft, and that doesn’t even take into account the production of the rest of the Allies. Over the course of the war, Germany produced fewer aircraft than the UK. Since neither the Kriegsmarine nor the Luftwaffe could make an invasion of the British Isles possible and there was no capability to starve the British, the Germans never had the capacity to defeat the UK. None of this should detract from the heroism of “the few,” but despite how desperate it seemed at the time the British were winning the Battle of Britain from the outset.