Revealing mistake: At the end when Sullivan is shot in the back while looking out the window, you can see blood come through the front of his shirt, meaning the bullets must have exited his body, yet the window he is standing in front of isn't shattered by the bullets that had passed through him. Also, immediately after this when Jude Law sets up his camera to take photos of Tom Hanks dying, the blood all over the glass is completely gone. The window is clean.
Revealing mistake: Towards the end of the scene where Connor shoots the wife and younger brother, he looks at his reflection in the glass at the front door. In the shot of Connor walking through that door onto the porch outside, you can see the icicles hanging from the gutter over the porch actually swinging.
Revealing mistake: Half the time the Colt 1911s in this movie are fake. In the scene where Tom Hanks is killing all the mobsters in the rain and it's in slow motion, if you watch all the guys with 1911s firing, there are muzzle flashes, but no slide movement and all the hammers are decocked. You can also see this in the scene where Hanks kills Paul Newman's son. It's interesting though, because the muzzle flashes aren't added in later - if you watch the making of it on the DVD, you can see Tom Hanks firing one of the guns - they're basically shooting smoke and a reddish, somewhat fire-crackery looking red flame.
Revealing mistake: When Peter and his mother are being shot, note that Mike Jr., standing outside the house, hears the sound of the shots just before seeing the flashes. The slight delay between the flash and sound is probably pretty close, but he should have seen the flash before hearing the sound of the shots.