Certain APs may cause heart problems if you are on them long term, I don't remember which ones, except clozapine which I think I read is especially bad for that.
Otherwise atypical APs are nowhere near as likely as the first gen to cause things like TD. With first gen chances of getting TD were like 80-100% while now they are only like 5-15%.
I haven't heard of any other long term issues. Some cause weight gain and I imagine over a long period of time that could become a serious issue as obesity kills and whatnot. Some cause elevation in prolactin (can greatly increase risk of cancer + make you gain weight) but that can usually be observed over a shorter time period.
You should be more concerned with the long term effects of being off an AP. Sz is a degenerative condition. Psychosis eats away at the brain (you literally lose grey matter) and the longer a person goes untreated the worse their symptoms will get until they are basically too far gone for anything to help them anymore. These people end up in some sort of long term residential facility for the rest of their lives. A pretty miserable fate. Meds prevent this degeneration.