Probably about time I mentioned Flight Through Entirety - http://flightthroughentirety.com/ The only Doctor Who podcast that I've managed to get through more than one episode of.

It's an Australian-based podcast with Nathan "Terribly Tiresome" Bottomley, Richard Stone, Todd Beilby and PS's Brendan Jones. (Todd and Richard rotate duties, which is much more confusing than it sounds) As the title suggests they're running through the whole of Doctor Who in order, plus a few extra bits mainly to fill up Colin Baker's short era.

It's amusing and insightful, with lots of references to German Expressionism, Tropes and Philip Sandifer. Recent episodes on the McCoy era have been particularly interesting, especially the Happiness Patrol which delves into the wider context of gay rights and some very personal recollections.

Given that I am incredibly judgemental about anything related to Doctor Who audios, consider this a glowing endorsement!