At the end of the film, Danny is loaded into the ambulance correctly (head first). As it drives off, we see him and his wife in the ambulance and his body is now in the opposite direction, as if loaded feet first.
At the end of the fight between Danny and the corrupt cops in Internal Affairs, Danny looks at them when he hears one of them has run out of bullets. When he looks at them, the door is pulled wide open, but the next shot shows them just pulling it open.
The sharpshooter puts a laser dot on Roman's head and the officers in the helicopter light Roman up with about eight lasers while he's standing in the window. Police sharpshooters don't use laser sights (i.e. red dot on target). They're good enough to not need them and don't want to tip off the suspect that he's in their sights. Any cops who do have laser sights (which is unlikely, but conceivable) don't put them on the target and keep them there. The sights are for rapidly getting the gun on target - not replacing proper sight picture.
When Roman and Sabian is browsing Niebaum's computer at his house the Address bar doesn't match the content of the other windows. The address bar says C:\niebaum\office files\ongoing investigations\*.* while the All Folders sidebar shows that C:\Office files\Accounts is selected. C:\ is labeled Niebaum, there is no C:\niebaum\ folder.
While browsing A:\Ongoing Investigations the explorer window says (A:) - Office files - Ongoing Investigations which doesn't match the contents of the All Folders sidebar.
Furthermore, although A: is full of documents they're marked with the windows icon, proof that no program has been assigned for opening or editing the documents as they were most likely done in haste.
When Palermo is told to take the shot, a closeup on his eye blinking through the scope is a stand in. This is evident by the brim and strap of a helmet and facial wrinkles that Palermo doesn't have. He has smoother skin and wears a backwards baseball cap.
The goof items below may give away important plot points.
While looking at the recordings from the wire in Nathan's badge, we see Rudy go to the one on the 12th and play that one. Danny then tells him to play the one the night before Nathan died, on the 12th. We don't see Rudy go to it, but a different recording is played.
When Roman and Sabian are hiding on opposite sides at the end of the hallway at Niebaum's home, Frost enters the home. When viewed from a mirror that Sabian is holding, the door closes, with the doorknob on the left side. Argento is on the left and Hellman is on his right. In true camera view, the doorknob is also on the left side of the front door.
When Frost thinks he and Chris have an agreement, he destroys the two floppy disks. When later Chris and the wounded Danny appear behind Frost in the door, Chris is holding a perfectly intact disc in his hand. However, it's possible the discs Chris gave Frost were only decoys while he kept the real one on him.