When Mac sits down at the chess table then removes the envelopes from his coat pocket and places them beside the chess board, the top envelope already clearly has a stamp on it, in fact the exact same stamp that Mac places over the microfilm a moment later.
The water tanker truck is emitting a lot of visible fumes as the fugitives approach it, but when Mac fits the hose onto the truck's tailpipe, there is no visible exhaust coming out of it. Then when he connects the hose to the water-line, the hose is spewing visible fumes again.
An ordinary coat-hanger would not be strong enough to yank a chair through a drywall barrier, especially if it was reinforced with wood laths and chicken wire.
When Mac, Penny and Stepan cross the border to Greece, Greek border patrol appears in a M422 "Mighty Mite". Greek Army, never had this particular vehicle. At the time, the army used Willys MB, Willys M38 and M151-MUTT and their variants.
This is set in Bulgaria, and the chase sequence involves driving down the same exact mountain road that had just been seen in the previous "The Enemy Within", which was set in East Germany.
When Mac, Penny and Stepan cross the border to Greece and the border patrol meets with them, the uniform the First Lieutenant is wearing, is a mix of late World War 2 and the 1950's-1967 period. Also his officer's hat is bearing the Royal Crown of the Kingdom of Greece. Greece is a Republic since 1975.
On Penny's passport it shows a birthday of Feb 20th, 1962, but in the 4th season of MacGyver (Secret of Parker House) her birthday is said to be Halloween (Oct 31st).