I must confess it was only years later that I realised the first episode was transmitted the day after Kennedy's assasination; well I was only eight at the time. However, I still vividly remember Susan's teachers, Ian and Barbara, following her home and finding the Tardis in a junkyard.

PS
There's reams of Doctor Who information and trivia on Wikipedia; e.g. the original transmission date was set for the 16^th November, but was put back due to technical difficulties - the doors of the Tardis not closing properly being one of them.