Continuity mistake: Phelps takes the tape from the recorder's right-hand spindle. When he opens the acid vat, we can see the tape he just removed back on the recorder - but on the left spindle. The tape he then drops into the acid doesn't remotely resemble the one he pulled, and when he drops it, the recorder's left spindle, where the full tape was in the last shot and where the empty reel should be, now has nothing on it at all.
Continuity mistake: While Barbara Bain is opening the puzzle box, Martin Landau is removing pieces of his disguise. First, he has a handkerchief in his right hand. Next, the handkerchief is gone and he is peeling off his left leather pocket, and the left leather lapel is already gone. Next, he removes his mustache with a handkerchief. Then, while removing the left leather lapel, the left pocket is back in place.
Continuity mistake: When the doctor tells the agent he has to step behind the shield while they take the pictures, you can see that Augie's chest strap has already been secured. The very next camera shot shows Cinnamin (as a nurse) just starting to secure his ankle area with the straps, and you can see the chest has not been secured yet. A second mistake in the same timeframe shows Augie's unconscious head turned to his left. When she starts to secure his ankles, you can see his chin pointing straight up.
Continuity mistake: When the Major checks the prison log book, the box next to 27 where the time entry should be is blank. He closes the book and holds it under his arm while conversing with a subordinate, and when he opens it again to show it to the other man, the time box has, impossibly, been filled in.
Continuity mistake: Tina demonstrates her contortionist abilities by crawling through the cubicle shelves in Briggs' apartment. A large orange cat figurine on the upper left shelf is brightly lit when she's doing her demo. The moment she finishes, though, the cat is in shadow and its orange tones are muted to brown.
Continuity mistake: Rollin strikes the duplicate diamond with a hammer and chisel, and it breaks cleanly into several pieces that fly out of the dish entirely. In the next shot, however, all the pieces are not only back in the dish, they're crushed into a fine powder.
Continuity mistake: After the gun goes off during his fight with Yankovski, blood appears on the right side of Rollin's mouth: it wasn't there a moment before. And a few shots later, the blood is on the left, then changes back to the right. (One shot in the sequence was, for some reason, flipped.)
Continuity mistake: When Briggs listens to the recording giving him his assignment, the tape isn't even threaded, so the machine shouldn't be playing anything. When he stops it, the tape is now threaded - but it's now a completely different tape reel on a completely different machine.
Continuity mistake: After Rollin is in a fist fight he has blood on the left side of his mouth. After a quick scene switch to another person when it goes back to him the blood is on the right side. Another quick switch and back to him, the blood is back to his left side.