I'm on but don't use Twitter but use Facebook a lot and have a fair few exes as Facebook friends, some serious relationship ones, some less so serious. There is nothing in it at all.
I'm single at the moment but it wasn't a problem when I was in a relationship, I don't imagine it's a problem for them either. I'm respectful to their partners, I'll comment on statuses or pictures from time to time but would never mention being an ex or relating to our time together if they are with someone (most of them are now married).
I'm not a jealous person though, my last ex still got on very well with his ex wife and her partner and we'd meet up sometimes or sometimes he'd go and meet her for lunch, I never had a problem with it.