I do the "full" check every flight, not just first flight of the day. Who knows what the previous renter didn't look at properly? - it is sometimes quite clear that they were not using the checklist.
Hmm ... except for the water in fuel check, which I do trust the previous pilot to have checked. Maybe I just have this expectation that if they hadn't checked it, and there was water, the aircraft would not be sitting there in one piece waiting for me?