During the first hand-to-hand fighting battle there is a shot of Solo (aka Smith) watching at the end of a line of guards. The first three guards next to Solo are shown looking at him intently instead of watching the action at the other end of the line. Later when the second round of hand-to-hand fighting is called for and Solo is indicated to be one of the participants, the guards are again looking at Solo as they did in the earlier shot. Thus the first shot was originally supposed to be a different view of the 2nd hand-to-hand fighting announcement.
Illya's fight on the balcony is one of the most obvious examples of a stunt double subbing in for the actor. You can clearly see the double's face and bad wig.
Part of what Illya is listening to goes, "... the mesons attain the speed of 10 million electron volts...," which doesn't makes sense, as electron volts has nothing to do with speed.
Fasik says that Muhammed the Turk conquered Constantanople in 1443. It was in 1453.
After Solo has been conscripted, Fasik is lecturing him and uses the words "insurgent legislature" which is obviously dubbed and mostly like by a different person as the sound of the voice is different from Fasik's.