The first thing is usually to point out how smelly Doug and Tony must be because they never change their clothes. This will usually be followed by a comment about the length of their hair and fingernails. Anyone who has actually watched the show will be able to give the answer that the two travellers are returned to the condition they were in when they were extracted from the RMS Titanic at the conclusion of their first adventure "Rendezvous With Yesterday" - it's a part of the transference process. Likewise any injuries that they may have suffered (such as Tony's damaged ankle in "Kill Two by Two") are undone. OK, I'm not denying that the real reason for this is so that they could use the same stock footage of Doug and Tony in the vortex week after week... but it is addressed.
Point two on the nit-picker's agenda is usually: "why do Doug and Tony always materialise in one of history's hotspots rather than someone's backyard or a field on an historically insignificant day?" The quick answer to which is that it would be pretty boring watching Doug and Tony sitting in a field scratching themselves for a whole hour - well I'd find it boring at any rate.
Point three is invariably: "How come every historical figure they meet - no matter where and when they hail from - speaks perfect English?" Likewise, this can easily be dismissed by pointing out that watching Doug, Tony and Historical Figure of The Week making hand signals and drawing pictures in the sand for an hour just to say "Hi", might make for pretty dull viewing. Anyway, surely it is conceivable that one or more of those many computer banks we see at Project: Tic-Toc might be doing the translating for Doug and Tony (a bit like the Universal Translator in the original Star Trek).
The thing that the nit-pickers always seem to forget is that THE TIME TUNNEL was a weekly television show meant to entertain the masses for 50-odd minutes a week. It was made in 1966 and so, yes, it has dated and doesn't look as sophisticated as the SF shows of today - but don't forget that those modern shows are building on what came before. Thirty-odd years on I can promise you that Babylon 5, Farscape and whatever Star Trek show is currently airing, will look just as dated and unsophisticated.