When I was at camp we had several cases of poison ivy caught through the public toilet seat. And the only two people who were poison ivy free said that they didn’t sit directly on the seat.
I’ve also heard you can catch “crabs” which are caused by parasites, not disease from toilet seats, but have no clue if this is true or at all likely, nor how easy it is to prevent if they’re in the stall.
A link to the Staff Report is appreciated. Providing one can be as simple as pasting the URL into your post, making sure to leave a blank space on either side of it, like so: http://www.straightdope.com/mailbag/mtoilet.html
I also wrote a staff report about poison ivy: http://www.straightdope.com/mailbag/mpoisonivy.html
It could be possible to catch poison ivy from a toilet seat if someone with a bad rash on his or her bottom sat down right before you. I wouldn’t think this would happen often.
Crabs can linger in sheets or towels and be spread to others that way. It would be unlikely to catch them from a toilet seat. Unless maybe you were sitting on someone else’s lap on the toilet seat.