There are quite a few errors in the beginning: from the camera rapidly panning on the paintings on the wall, which are simply hung upon a protection-less plain wall painted blue, to the careless way the antique paintings are handled. Also, when removing the nude, two large nails remain on the wall. No one would hang such priceless art on two single nails as shown. Finalizing the intro blunders, a female extra at the market when Banacek buys fruit, is seen staring at the camera.
While Banacek is talking with Casey in the dispatch yard, tall mountains are seen in the distance. There are no such mountains visible from Boston.
When Larry Casey is shooting at Banacek, at one point he shoots some holes in barrels of some kind of fluid. Two issues: 1. The third barrel from the right is struck twice, and has two streams flowing out of it, one higher than the other. The problem is that the stream from the higher hole is shooting farther than the lower one. This is the classic mistake. In this situation, the higher hole has less force behind it, so it should not shoot out as far as the lower one. 2. The streams are flowing out continuously from sealed barrels. The streams should be stopping and starting to allow air to flow into the barrel and displace the fluid leaking out - or the fluid should be dribbling down the outside of the barrel, not shooting out the way it is.
The cars in the airport parking lot have California plates.
When Banacek identifies the "ancient text" Felix is trying to translate, because he knows it from a Polish operetta of the 20s his father used to sing, Felix tears the document into four pieces. He never stops to consider that the document might have been an ancient source from which the operetta's libretto was drawn, a very unlikely oversight for an expert in rare books and documents.
When they go to see Katz he was playing the violin. When he opens the door he is holding the violin. However, there is trace of rosin on the bow or violin.