When Jane is giving Fred that vile drink, you can see the band-aid on his head (1:00) where he got hit by the globe that Eddie would later throw (1:05).
When Fred visits Eddie, Fred has a pool stick in his backpack, but it is gone when he walks away.
When Fred first enters Jane's office, there is a card on her desk (at around 52 mins) that Fred takes (at around 57 mins) but which is soon back on the desk (at around 1 min).
At the end of the film, Jane shows up with a very large birthday cake for Fred. Moments later, Fred blows out the candles on it and it is suddenly much smaller.
Fred's backpack strap is down on his elbow when he's talking with Eddie in a longer shot (76:42-76:55), but is up on his shoulder in the immediately preceding and following close-ups of Fred.
There are several errors in simple mathematics in the movie: Firstly, Damon "The Mathemagician" Wells correctly states that there are 25 228 800 minutes in 48 years (but 25,246,080 minutes if one counts the 12 leap-days that would occur in any span of 48 years that doesn't include a century year - only century years evenly divisible by 400, like 2000 but not 1900, are leap years), then says that this is 151 368 000 seconds. This is clearly wrong as 25 228 800 x 60 is 1 513 728 000 (more than 10 times as much). Furthermore, Fred says that the cube root of 3 796 466 is 156 although 156*156*156 is 3 796 416.
When asked the question of what factors the number 3,067 has, Damon replies that the number has no factors because it is prime. That is incorrect. Every prime number has two factors: 1 and the number itself. Yet the moderator accepts his answer of "no factors" without even asking for clarification.
(At 19:31-19:36) When Fred is playing the piano, a close-up of his hands show hands that look completely different (and much larger) than his own. They are obviously hands of a piano-playing double.
When Gina is trying to convince Dede to go with her to Orlando to take a job at a hotel there, she shows Dede a picture postcard of the hotel. The photo of the hotel has an ocean and beach in the background. Orlando is in central Florida, not on the coast.
When Dede calls Tate from the hotel in Orlando Florida, the public pay phone does not show the locally proper 407 area code on the phone's label above the dial pad.
(at around 50 mins) During a short part of Fred's piano piece, the notes he is hitting are obviously different to the ones that would be needed to make the sound. There is a part where the music is going down, but Fred's hands are moving up the keyboard.
When Dede starts the mouth to mouth resuscitation she immediately tries to breathe into the child's mouth. The proper way is to check the mouth for any obstruction and then lift the neck and let the head fall back to ensure the airway is open before breathing into the mouth.