Um, it's a show about a man traveling through space and time in a 1950s Police Box and fighting aliens, and the radiation-proof glass is what you had a scientific problem with? It's a show that you watch for the characters and the adventure, not the science (oh, and nothing in that show is less realistic than Star Trek).
Seriously, though, it's a great show. Yes, some episodes are bad, but if a TV show is only as good as its worst episode, well, then no TV show ever made is good. The Steven Moffat episodes are some of the best things to ever happen on any TV show in history (and he's taking over as showrunner... to which I say "yes yes yes yes YES!"), and most of the others are great too. Yes, there are sometimes problems with continuity and logic, but there is a surprisingly deep philosophy running through the show (read Jacob's recaps [http://www.televisionwithoutpity.com/show/doctor-who/recaps.php] if you don't believe me), and it's a damn good time as well.
Seriously, though, it's a great show. Yes, some episodes are bad, but if a TV show is only as good as its worst episode, well, then no TV show ever made is good. The Steven Moffat episodes are some of the best things to ever happen on any TV show in history (and he's taking over as showrunner... to which I say "yes yes yes yes YES!"), and most of the others are great too. Yes, there are sometimes problems with continuity and logic, but there is a surprisingly deep philosophy running through the show (read Jacob's recaps [http://www.televisionwithoutpity.com/show/doctor-who/recaps.php] if you don't believe me), and it's a damn good time as well.