TARDIS Crew: The first Doctor (William Hartnell), Vicki Pallister (Maureen O'Brien), and Steven Taylor (Peter Purves)
The Plot: The Doctor and Vicki find themselves traveling alone, Ian and Barbara having found a way to get home at the end of the previous story, "The Chase," when they discover that Steven, a marooned astronaut they met during that story has stowed away on the TARDIS. Though grateful to be rescued, he refuses to believe the Doctor's claims that the TARDIS is a time machine, a belief he feels is strengthened by his discovery of a 20th century wristwatch in 1066 England. Turns out there are a lot of anachronisms in 1066, including but not limited to a gramophone, a toaster, an unscheduled Viking invasion, an atomic cannon, and a man disguised as a monk who has a TARDIS of his own and wants to change the course of the Battle of Hastings, preventing the Norman conquest.
The Thoughts: Lots of firsts in The Time Meddler: the first time we see the Doctor traveling without any of his original three companions, the first time sci-fi and historical elements were combined in the plot of the same story (commonplace from the Troughton era onward, of course, but back in the day, stories were either one or the other), and of course, with the introduction of the Monk, the first time we meet another Time Lord, renegade or otherwise. And the Monk makes a very interesting foil for the Doctor; most of the other renegades we eventually meet are downright ruthless, but the Monk has it in his head that he's actually helping the history of Earth by trying to change it. And so we see the Doctor, himself a renegade of sorts and obviously the original free spirit, take on a role we see him take more and more over the years, especially in the new series: the authoritarian preserver of The Rules. And, of course, William Hartnell is perfect in this regard.
But at the same time, we see that another facet of Hartnell's Doctor has emerged since the series beginning: he can still be gruff, and he does not suffer fools gladly (or at all), but he is also now totally the Grandfather. He's happy that Ian and Barbara have finally found a way home, but is clearly sad that they're gone, and considering how often he talked about abandoning them (or actually tried to do so!) in the early episodes, is quite a change. He's all warm and cuddly with Vicki, inviting to Steven... yeah, this is a changed Time Lord to be certain.
As for Vicki and Steven... yup, they're the Doctor's companions, alright, and that's pretty much all you can say. She's the spunky, intelligent, capable, cute girl who's also a good screamer when the scene calls for it, he's the guy who gets all the action scenes Hartnell can't handle, and they both ask "What do we do now, Doctor?" with the proper amount of conviction. They're likable enough, sure, but fairly generic. But I tend to think that of most of the early companions, anyway - for my money, the first one with any real personality is Jamie McCrimmon, and only once they start actually writing for him, rather than just giving him some of Ben Jackson's extra lines.
Finally, the best thing The Time Meddler has going for it? It's short! So many Hartnell stories (Troughton's, too, for that matter) just go on and on, padding just a few episodes' worth of story out to 6 or 8 or more installments, and I always found them so boring. In fact, I prefer the first Peter Cushing Dalek movie to the original Who story it's based on specifically because the movie is considerably shorter! But this story's 4 episode running time is just about perfect. It moves at just the right pace, and very little extraneous-to-the-story material makes it to the screen. I do loves me some economical storytelling in early Who... it's a shockingly rare occurrence.
And to think, for years I thought I didn't like William Hartnell's version of the Doctor. Turns out my real problem was with the script editor.
Overall: There's a lot to like in The Time Meddler. Not only is it historically important to the series, it's also a lot of fun and mercifully short for the era. I somehow missed this one in the PBS rotation a couple of times as a kid (admittedly because I'd always reach a point where I wished they'd just get to the three Troughton stories they had), but now it's my favorite Hartnell story of all. Trust me, it's the William Hartnell story for people who think they hate William Hartnell stories.