I have all the 'dance with so-and-so achievements but I messed up and didn't refreash for the conversations so it thinks I'm still waiting on the convos and own't let me progress with the man who just repeats:

Oh, you, hello. Unfortunately, I have no time to talk - I'm just looking for the first minister so I can have a, erm, document of importance signed. Very urgent you understand, no time to chat.

How do I progress?

Maybe you can look through your internet history to find the urls you used to dance with the NPCs and refresh them? (hopefully they'll still work) Otherwise, I guess you'll have to find new invitations to use. Which sucks of course, but I wouldn't really consider it a glitch unless there's literally no way for you to progress the storyline.

Is it known if there is a further step with Inspector Thorpe right now? There might not be.

raises a good point xD I've only found one invitation so far so I'm a bit behind, but if you want to know what to do next you could read the Masquerade plot thread if you don't mind spoilers: http://subeta.net/forums/view/895545

Edit: Ok I've caught up now and found out that, yes, you need to unlock a new part of dialogue with the inspector to continue.