Are you SERIOUS? I assume this varies by state?? I am ALL FOR having a sex offender registery, but I think it's a shame that some young people are lumped into the same group (or even some dumb older ones, or older ones who couldn't "hold it" any longer). That's crazy and ridiculous!
Each state has it's own requirements.
In Iowa, yes, it is possible to get on the sex offender registry for public urination. And, at least for awhile, the law made the registry retroactive.
It caught a friend of my brother. When he was out with my brother hitting the bars, being stupid young things at 18 (this was back when the legal drinking age was 18), they left their last bar of the evening and didn't have enough cash left to meet the cover charge to get into another bar so they headed home. As they were heading home, the effects of too many pitchers of beer caught up to them.
Due to the time, the only places open in the area were bars. Due to the cover charges, none of them could go into any of those bars. So they used the alley. Three of them (including my brother) were done and the fourth of them was still going when a foot patrol officer entered the alley.
He ticketed the last guy with "lewd and lascivious display" on the grounds that it was a public alley and a child could have seen it. Any child venturing into a totally unlit alley at 1:30 am on a Friday night had a lot more to worry about than seeing a drunk guy peeing.
I'm not excusing my brother or his friends, it was a stupid and gross thing to do. But it wasn't done by future predators, it was done by a gaggle of stupid 18 year old boys.
He paid up his fine (as I recall, it was less than the $20 court charge) and forgot about it.
Went through college, went through medical school, became an orthopedic surgeon specialising in knee injuries. And then one day, he got a call from a neighbour who knew him asking him why he was on the sex offender registry. Took him close to a year to apply to have his previous conviction expunged (he had no further convictions, not even a speeding ticket) and get his name removed.
And that, to me, was even stupider than an 18 year old peeing in an alley because he forgot to visit the rest room before he left the bar.