Little mistakes they could have fixed
The one that I noticed that bothered me was the night Sam died, which was supposed to be in 2005. The Boston Red Sox clip that they showed with him watching the game featured Dustin Pedroia, but Pedroia didn't play for the Boston Red Sox until 2006. They easily could have picked a clip from the night he died, or at least the same summer.
There are lots of little mistakes that others have picked up on. All of them little and could have easily been fixed. If they just paid a little bit more attention, the film would have been better with a higher rating. Everytime there's some mistake which a viewer picks up on, it lowers their opinion of the movie by at least a star. At least I think so, and subconsciously at least.