I am still slightly concerned over one woman but that's maybe because I don't like to see a very pretty woman talking in an overly familiar way to my DH and maybe they have never met in RL and my instincts are out on this one
You also have to remember that, if they have been twitter friends since the beginning, they are now in a nearly 10 year friendship, so while it's overly familiar to you because you're seeing it from the outside where it is now, it has developed to this point and wasn't always at this stage. I didn't tell my Ex (when we were still married & together) about everyone I talked to on Twitter, because he didn't have/use twitter and because it was just people I talk to on the internet ... much like any online forum.
To me it just seems like you don't quite understand how Twitter works and it's making you feel paranoid about perfectly innocent exchanges you have seen.
I guess what I am really saying is that I am rather shocked that DH has an aspect to his life I knew nothing about and am a bit miffed he tells people there things that he never mentions to me.
So you need to talk to him about that - sometimes being on the internet is our chance to, not quite reinvent ourselves, but to be freer than we have to be in public - take this very thread on this very forum, would you talk about your issues with your DH being on twitter with a load of random people on the bus? No, I'm fairly certain you wouldn't, but on the internet there's that little slice of anonymity or distance that makes you feel like you can safely discuss things with, what are essentially, total strangers. This happens on Twitter too - stuff people wouldn't say IRL they feel comfortable putting on the internet as whilst people obviously know there is a real person on the end of the other twitter handle they are talking to, it's a little less personal and people feel they can either be more honest or less inhibited about their discussions.
What about his conversations are you "miffed" about? Is it that he's talking about family issues or personal problems that he's never told you about, because in those cases I think you are definitely within your right to be a bit upset that he felt he could share that with strangers but not his wife especially as those things are going to affect you too. Or is it that he's telling people random stuff that he's just never thought to tell you about but that ultimately had no bearing on anything or effect on your life and so really aren't worth getting upset about.
He's clearly not got anything to hide as he doesn't have a locked account or has ever actively hidden his twitter from you, he's just not gone out of his way to include you, so perhaps the issue is less his Twitter life and more the fact you're feeling left out of it?