Plot hole: Explosions are very predicable and leave very clear traces after detonation, and the precise epicentre of a small nuclear explosion could be established within a few meters. Experts from the United States military could show that the nuclear explosion originated outside the airbase, and the evidence they could show (aerial photographs, etc) would be irrefutable. They could even invite their counterparts in the Russian military to see for themselves. The only way Petrofsky's plan could have worked would be if he could somehow get the bomb inside the perimeter of the airbase - not a terribly likely proposition.
Continuity mistake: At the traffic hold up, when Caine spots Brosnan speed away in the blue Ford, Caine races back to his transit van and uses some creative off road driving to catch up. During this scene, damage to the van seems to appear and disappear, most noticeable is the license plate.
Continuity mistake: When the troops are closing in around the house, Pierce Brosnan is listening to Tchaikovsky's 4th Symphony. At one point the music is reaching the end, then it cuts to a shot of a soldier moving in closer, and when it cuts back the piece is finishing - however, the difference in time between the last bit we heard and the end isn't long enough for it really to have finished.
Visible crew/equipment: When we first see Brosnan in the blue Ford escort you can see the boom mike reflecting on the bonnet near the ford badge.