Factual error: The Russians use a beeping "radio direction finder" to find the partisans by detecting a bug swallowed by the Mayor's son. In closeups the "direction finder" is seen to be an impedance meter (used for measuring AC resistance) - it's labeled "X=(down arrow) x (up arrow)(omega)". X is the standard abbreviation for impedance, omega means "ohms" (the unit of impedance/resistance), so the label says "impedance is lower dial times upper dial, in ohms". There is a piece of spiral twisted wire across the terminals of the impedance meter which would be useless for radio direction finding.
Factual error: When the Russian tank rolls up to the two gas pumps, the crew have a choice of regular gasoline (as indicated on the pump), or Good Gulf (a premium gasoline). And in fact one of the tankers tells the attendant, "Gasoline." The trouble is, all Soviet tanks, from the T-34 up through the T-80, have diesel engines for safety reasons.
Revealing mistake: In the beginning of the movie, when the teacher is shot, the impacts on his chest are out of sync with the actual gunfire. First, we see the soldier start shooting, but he fires several shots at point blank range before the bulletholes and blood appear on the teacher. Also, as the angle changes, the teacher falls backwards with more impacts appearing on his chest. The problem is, the soldier has already stopped shooting, and there is no other gunfire to be heard.