Well, a lot of it IS pretty nonsensical; it's not hard sci-fi at all and in some ways doesn't even fit the sci-fi definition, but, y'know, time travel and aliens= sci-fi to people. If you keep in mind a) when the show started they did often have to work with ridiculously low budget props (including their main villians having plungers) and while the budget values now are better, they seem to have kept the "camp" factor for humour reasons (or something, I dunno, I know I like it but I also watched the original Lost in Space show "for the lulz" when I was a kid, so I like it) and b) in the 70's, Douglas Adams wrote a few eps, himself, which of course complimented the oddball absurdist British humour, you'll see that often, no, there isn't much to really GET.

(It also makes it easy to poke fun at, which is why these comic ideas have been coming steady and fast. D: People seem to love 'em here, though!)

Oh, and I apologize for that guy you mentioned on Twitter who said you were lame for not watching Doctor Who. While I'm sure idiots like that exist in the fandom because it's a large fandom, none of the people I know are like that.