We have a weekly Slow Session in Edinburgh with Nigel Gatherer, one of the Scots Music Group tutors, and I believe Glasgow Fiddle Workshop (not just fiddles) and SC&T in Aberdeen do the same. It really is a great introduction to session playing for folk learning instruments, and a chance to learn the tunes properly before upping the tempo and moving on to other sessions in the area. (Tho' of course, some tunes don't need "upping"!) Some pretty competent players even choose to stay at the Slow session, as they prefer the gentler pace.
Nigel also produces a great series of A5-size books of tunes and sets - very handy to carry around for those that need to have the dots or chords in front of them. And he has a fantastic website with loads of tunes to look at for free.