The level of the drink in Truman's glass changes between shots when he is talking to Patch.
During the welcome scene at the school, the green folder on the desk/counter moves between shots.
Position of Patch's hands and fingers in the first "How many fingers do you see?" scene.
Hoffman's character tells Patch to get a suit to appear before the medical board. Patch was wearing a suit at Carin's burial, and Hoffman saw him.
The answering machine in the movie didn't exist in the 1970s.
The Pablo Neruda poem used in the film (set in the early-to-mid-'70s) was not translated into English until 1986.
When Carin and Patch are walking together discussing his time spent in the psychological institute we can hear them talking but the actors mouths are clearly not moving.
At the Gesundheit Institute, one of the patients is watching the Marx Brothers film Duck Soup (1933). But the audio track doesn't match the portion of the film shown on the television screen.
When Patch tells Dean Walcott he wants to see his records, the Dean replies that they are confidential. As Patch walks out, the Dean has his head down, he is writing and his left arm on the desk, before he lifts his head, moves both his arms and prepares to get out of his chair. However, when the Dean says "Only the staff...", he is still writing and his left arm is back on the desk, before he stands up.
Camera and boom equipment are visible (and in motion) in the door window as the gynecologists are approaching the door between the paper mache "legs" that Patch Adams prepared for their arrival.
Mitch rats on Patch for cheating since he never cracks open a book but still nearly got 100% in the course. How does Patch possibly score this high? The movie never shows Patch studying or reading.
Patch says that humans are the only organisms on Earth that kill their own kind. This is not the case. Chimpanzees also do this, for example. In fact, it's much harder to find a species that doesn't kill its own kind than one that does.