Corrected entry: The Brigadier met the Doctor previously in 'The Web of Fear' and 'The Invasion', both Second Doctor (Patrick Troughton) stories. In 'The Web of Fear', the TARDIS was trapped in the tunnels, not to be seen until the end of the story...and in 'The Invasion' the TARDIS was invisible. So how does the Brigdier know that the Police Box is anything but an emergency phone booth?
Corrected entry: When he meets the Doctor for the first time, the Alternate version of Stahlmann refers to Lethbridge-Stewart as "Brigadier", even though his rank in this universe is "Brigade Leader".
Correction: Stahlman mumbles the line somewhat, but he's definitely saying "Brigade Leader."
Correction: At the end of The Invasion, the departure of the TARDIS, now visible in its normal police box form, is seen by UNIT's Captain Turner. As the Brigadier's right hand man, I'm pretty sure that Turner would relay the information about the TARDIS's appearance back to the Brigadier.