During the high speed boat chase, the camera helicopter's landing skid comes briefly into view as the camera is following the bad guys' boat. It's visible in the bottom right corner, and is very noticeable.
During the high speed boat chase, MacGyver picks up some petrol (gas) cans with "BENZIN" written on them in english. The scene is set in Russia, so the writting should have been in Russian.
After MacGyver helps Alexander Karsov escape the more secure cell-block and takes him back to the less secure patient dormitory, there is a scene where he plans to distract the male nurse in order to smuggle Karsov into the room. Watch when MacGyver says: "Come, I'll show you the open gate"; there is a fast moving, but clearly visible, shadow high on the room's wall, right behind where MacGyver is standing, and judging by its shape it is a microphone