3) Be prepared to clean the underside of the aircraft if it is at all muddy - so best pick a day when your chosen airfield is firm.
3b. Don't forget the inside of the wheel spats. If the strip is very muddy, might be a good idea to remove them altogether, but check the POH for reduced cruise speeds. If it's a rental, talk to the owner first.
The other (obvious) thing to watch out for is that grass strips are usually, well, grass in a surrounding of grass. It's much harder to spot the runway, usually. Plus they are normally not ICAO marked with centerline & edge markings, approach lighting and so forth. It might help to view the strip in Google Earth before you set off and if you're not completely sure about the layout of the runway, do an overhead join or a low-level go-around before you land.
You'll also find that occasionally grass strips limit the strip width to less than half the available width by moving the "doghouses" (either black/white checkered or red/white checkered, doghouse-like structures) so that the rest of the strip can recover itself. Or they move the doghouses so as to create a variable, displaced threshold. So pay attention to the exact location of these doghouses (or other markers) so you land at the proper stretch.
Also higher chance of bird and other animals around as grass strips are normally found in rural areas.
It's a VERY sad refelection on the USA schools that not one of JAA approved ones will allow (or train) their pilots to land on grass.
Can't really blame the US schools for that. I learned in Florida and to the best of my knowledge there was exactly one grass strip within a reasonable flying distance. This one was a private field, requiring PPR and landing fees. Yes, there was a stipulation that students were not to land on grass (citing insurance reasons) but if there was a good enough reason, this could be waived. I think if I had insisted, I could have done a few dual, and maybe even solo landings and take-offs from grass.