Some prints eliminate the opening "Embassy Pictures" logo, as well as a few seconds of footage in the bar scene, including the drunk's dialogue "Let's have a toast...to toast! I love toast..." and the beginning of the song "By the Light of the Silvery Moon". Most prints just cut into the scene in the middle of the song verse.
The original, network television broadcasts added some outtakes (more fuse bumbling by Franz Liebkin) near the end, between "The quick fuse?!" and the eventual explosion. The padding was probably to balance some censorship cuts in the running time.
The 2002 DVD release includes an alternate blow-up-the-theater sequence. Franz Leibkind stomps out "ze quick fuse" after lighting it. He then switches to electrical detonation from outside the building. This fails. When Leo, Max and Franz go back into the basement to see what went wrong, the drunk from the bar comes along. Thinking that the detonator handle is a shoeshine stand, he props his feet up on it...
The 4-Front UK video release omits a couple of lines from Leo Bloom's hysterical attack in Bialystock's office (with a very noticeable edit), considerably shortens the scene with Leo and Max in the bar with the drunk (most of the 'Light of the Silvery Moon' number is missing) and deletes about half of the scene where Franz attempts to blow up the theatre. All these scenes are intact on the print regularly screened by BBC-TV.