For me, I pay extra attention during practice/rehearsal. I also make notes (cheat sheets) if the songs have a lot of changes, stops, etc, which helps me remember. I also keep things simple until I know the song well enough to start adding more complicated fills, etc. I also watch the band leader much more than normal.
It sounds like these are all originals, so I suspect getting a disk of the songs is out of the question....?
I do keep things simple and pay a lot of attention to the guys, plus we rehearse in the guitarist's studio so we record everything... the problem seems to be that the songs start changing a lot and we keep adding stuff. Maybe it's because we've only gotten together 3 times so far... maybe I'm expecting too much too soon?