Revealing mistake: During the St. Patrick's Day parade, Kimble removes his coat. In the next scene, he hasn't got the coat anymore, and he HASN'T dropped it. Don't be fooled. If you look to his right in the scene just after he takes it off, you can see a man carrying a coat that is the exact same colour and design. I assume this guy is supposed to be hiding the coat from view, but you can plainly see it. The guy is wearing a green hat. Kimble had no time to give it to him before the scenes changed.
Revealing mistake: When Kimble jumps from the dam, the falling body is clearly a dummy, otherwise he broke every single bone in his body before he even jumped.
Continuity mistake: Kimble dyes his hair very dark to escape detection and dyed hair fades over time. For the rest of the movie his hair noticeably goes from darker shades to lighter shades and back again showing that the scenes were shot non-sequentially on different days with a fair amount of time in between.