From Wm. Shirer's 'The Rise and Fall of the Third Reich', which is sourced from diaries of various Nazi officers as well as the Reich's secret papers captured by the allied forces:
"The generals who assembled at the Führers headquarters at Ziegenberg on the evening of December 12th, minus their briefcases and revolvers, found the Nazi warlord, as Manteuffel later recalled, "a stooped figure with a pale and puffy face, hunched in his chair. His hands trembling, his left arm subject to a violent twitching which he did his best to conceal. A sick man... When he walked, he dragged one leg behind him."
Hitler's doctor noted in his diary on August of 1941 "Left hand shows a tremor." This first-hand account is likely the chief reason that they chose to include this in Downfall. But there is also film of Hitler where the tremor can be seen.
Several doctors (Dr. Tom Hutton and J. L. Morris chief among them) have concluded that Hitler must have been suffering from Parkinson's by, and likely before, 1941.