The word "corp" on the military truck in the opening scene has period after it as if it were an abbreviation for the word corporation. In military parlance corp or corps is body of soldiers. The word on the truck should have no period after it.
When the two guys break into the apartment, it's obvious that Peter Graves is replaced with a stunt double. The stunt double clearly misses when he "punches" the bad guy in the face.
The shot of the two hit men driving to Annette's apartment so they can kill Jim, you can see sunlight on the buildings in the background, however when they arrive at Annette's apartment, it's once again nighttime.
When Willie steered the Ford truck in front of the vehicle pursuing Phelps and then cranked the starter to give the impression of a stalled truck, it was the sound of a Chrysler car starter not the sound of the Ford truck starter.
The shadow of the boom mike can be seen passing along the front of the truck when the truck stops at the Admiral's Garage for refueling, as Jim and Willy ambush the drivers.
It's impossible for Al to have given Art Stafford Annette's phone number because he had previously torn the sheets from his address book.
Boom mike shadow visible on door as Doug (Bert Convy) leaves Lisa's flat (35m 12s)
Towards the end, Barney clearly says "Where's Jim Rayburn?" but he should have said "Where's Tim Rayburn" which was Jim Phelps's fake name at the time. (46m 25s)