I've watched lots of shows being taped over the years (at Queen Margaret Drive - yet to visit PQ), and nearly all had sections of pre-recorded material played back to us.
Yes, with sitcoms there are a number of things that will got shown to an audience on screens: anything complex (either technically or in terms of performance or props), scenes that have a reveal or an element of surprise and of course external scenes.
On sketch shows - the likes of Little Britain, Mitchell and Webb or Armstrong and Miller they can only get 2 or 3 sets maximum in the studio so will only perform a few sketches live in front of the audience. The pre-recorded sketches are packaged up into 10-15 minute sequences and shown to the audience during the costume changes.
Everything is filmed out of order though, obviously if there's a repeating character they might do all their sketches on one night while his house set is up. Also if there's a running joke that doesn't make sense without the set up from episode 1, all the audiences might get shown that.
There is another important by-product of this process - sketches get chosen for the final series according to how they go down with the audience, if no-one laughs it will get cut. They'll normally edit them together so the strongest sketches go in episodes 1 and 6, the second best in ep 2 etc. Some sketches might not get a laugh on one night but will on another so they'll obviously broadcast that one