Plot Hole: The lynchpin of the plot makes no sense whatsoever. In an effort to defuse international tension, the superpowers would allow Britain (which was not neutral in the Cold War) to publish the codes that would allow anyone in the world to launch their nuclear missiles?
The Doctor mentions that the Alpha Centauri Table Tennis club members have six arms. This is a subtle reference to The Curse of Peladon and The Monster of Peladon where there is an Alpha Centaurian and he has six arms. He doesn't look like much of a table tennis player, though…
Plot Hole: The elite UNIT soldiers not only let a slow-moving 3-metre tall silver robot escape from them, at various points during the firefight, they are shooting at each other.
The Doctor: [bamboozling a guard] Where is that pass? It must be somewhere. Key to the city of Skaro, no? Pilot's licence for the Mars-Venus rocket run. Galactic passport? Do you travel much? Honorary member of the Alpha-Centauri Table Tennis Club. Very tricky opponents, those chaps. Six arms and of course six bats, really keeps one on one's toes.
The Doctor: Aren't you forgetting that in science as in morality, the ends never justify the means?
Brigadier: Well, naturally enough the only country that could be trusted with such a role was Great Britain.
The Doctor: Well, naturally. I mean, the rest were all foreigners.