It is interesting how public washrooms are gradually becoming more and more automated - auto toilet/urinal flush, auto water/soap dispensing - but I see 2 more possibilities:
Ever go into a public washroom which uses paper towels for drying your hands, which also has a garbage can with a single spring-loaded
flap? Usually it is stainless steel, and I hate 'em. Yo have just washed and dried your hands, yet you now have to use the back of your clean hand to push and hold open the flap, which of course is undoubtedly a bacterial filth-trap. I don't do it. I usually just carry the paper towel and throw it on the floor near the door, AFTER I use it to open the door. I've seen too many guys come out of the STALLS(!) and head straight out the door to even think of touching a public washroom exit door handle.
So idea #1, and it's nothing revolutionary - have the garbage container flap use an electric eye device to spring open, and the same thing for the door, so that you can keep your hands clean after they are washed.
Number 2 ( no pun intended ) - the stalls themselves. Think about it, you have zillions of guys who have just wiped their arses, haven't yet washed their hands, and are all touching the same latches/bolts etc. I know, I know, you are about to wash your hands anyhow, but still..
You can't use an electric eye because it might get triggerred inadvertently either by a movement (lets not get into THAT!) or even an insect. But why not use a button controlled by your feet that you need to step on to open the door?