100,000 BC - S1-E1
Continuity mistake: When Ian and Barbara enter the TARDIS for the first time, Susan operates the door switch. Later on, when the Doctor electrocutes Ian, he uses the exact same switch.
The Daleks - S1-E2
Continuity mistake: In episode three, Temossus claims the Thals have been travelling for four years. But in episode five, Ganatus claims it is one year.
The Daleks - S1-E2
Continuity mistake: The Dalek the crew ambush in episode three has a magnetic block in its sucker and, after the attack, a mud-covered eyestalk. At the beginning of episode four, the eye-stalk is visibly clear of mud, yet is later seen plastered with mud once more.
The Daleks - S1-E2
Continuity mistake: The Doctor removes his coat and it's left in the prison cell but in the brief shot of the Doctor and Barbara pushing Dalek Ian, the Doctor is inexplicably wearing his coat again.
Continuity mistake: Susan's socks disappear during the opening credits.
Marco Polo - S1-E4
Continuity mistake: The caption slide at the end of episode two reads: 'Next Episode: The Cave of Five Hundred Eyes'. While the title slide comes up at the start of episode 3, it simply says "Five Hundred Eyes".
Suggested correction: The original episode survives only as audio, so this mistake, if correct, must apply to one of the reconstructed versions (either telesnaps or animation), which probably therefore needs specifying.
Continuity mistake: In episode one, Barbara activates her travel dial only seconds before the others. But in episode two, she's been at Morphoton for quite some time - long enough to change clothes, pick fabrics and get food.