Preston performs the break-in on New Year's Eve. He is later assigned to Airports and Ports, discovers the Polonium disc from the courier off the ship, has it identified, writes his report, and is subsequently suspended from duty. However when he goes home and his son is playing, there is a Christmas tree with lights on in the house. This means that unless he has ignored the tradition of removing Christmas decorations by Twelfth Night - January 6 - all of the above would have taken place in 6 days. As this would have included January 1 - a Bank Holiday - and at least one day of a weekend, this timescale is highly unlikely.
When Michael Caine decks the two punks on the train for their racist behavior, look closely as the train pulls into the station. On the left of the screen seen through the train window is the roundel sign for ALDWYCH (which is probably where it was shot). As he leaves the train, the sign suddenly changes to PADDINGTON.
During the film, a KGB agent is said to be traveling by rail from London to Colchester, yet he is shown catching a train from St Pancras Station, which serves the Midlands region of England. The only way to travel by train from London to Colchester (which is in East Anglia) is from Liverpool Street Station.
In the NCO club, a US Air Force Chief Master Sargent is standing behind Ross with his hat on. When indoors and in uniform military members are required to remove their hats (except for armed guards and other special conditions). In most on-base clubs, this breach of protocol would require the offender to buy a round for the house.
Valeri and Irina assemble the bomb with their bare hands. Irrespective of the radiation risk, uranium is highly toxic by skin contact - they would both have become very seriously ill shortly afterwards.
The whole antagonists' scheme is doomed from the beginning. The detonation epicenter of such bomb can be traced down to 10 meters or better - one only needs to check where the circle of destruction has its center point. Therefore, it would have been immediately known that this was not a bomb from the base, which would automatically put the suspicion on the Soviet Union. This hole could have been rectified if Pavlov had to smuggle the bomb into the base.