The Keys of Marinus. This William Hartnell-era story is actually one of only a handful of classic Who that, even taken in the context of the time, low budgets, etc., I rate as below average-to-poor.
The Web Planet. This one mostly due to the silly giant moth costumes worn by the alien actors. According to the BBC online story guide this story was enough to make William Russell (Ian Chesterton) decide to quit the series after 2 years as a companion. And it was evidently the "A Night in Sickbay" of its time as the first episode was the highest-rated classic Who episode ever (something like 13 million!) but the ratings dive-bombed in the subsequent weeks.
The Horns of Nimon. Definitely one of the lesser Tom Baker stories. Still worth seeing because it's a Tom Baker story, and has Lalla Ward as Romana looking cute as ever, but it's not really a good one for new viewers.
Other than that, I'd actually recommend avoiding the Colin Baker and Sylvester McCoy eras altogether for new fans. That does not mean to imply that all of their stories were bad. Far from it - Remembrance of the Daleks, the 14-episode Trial of a Time Lord, and Vengeance on Varos rank in my top 20, easy, and there's also sentimental favorite The Two Doctors - but owing to the circumstances behind-the-scenes, plus the fact the show started to play with the character of the Doctor a bit, especially as the "Cartmel masterplan" kicked into gear, I don't really think these eras are particularly good for "inexperienced" Who viewers. They're better suited, I think, for viewers who have already watched a lot of earlier Who. For example, you can't really appreciate Ace until you've experienced characters like Jo Grant and Polly. Remembrance of the Daleks' best moments are meaningless if you haven't watched any other Daleks stories. And 'nuff said you need to have some Troughton under your belt, or at least The Five Doctors or The Three Doctors, to make any sense out of "The Two Doctors"...
In fact, although "franchise fatigue" was definitely a factor in Doctor Who's ratings collapsing and the show ending in 1989, along with a number of fairly poor or (in the case of Ghost Light definitely) incomprehensible episodes, the fact the final 5 years or so of Doctor Who offered very little in terms of "jumping on points" for new viewers was probably as big a factor in the show expiring as anything else.
Alex