Uh... I thought I was beginning to see the dreaded freezes typical of Bethesda games with big save files. In a short gaming session, I had 3 console freezes. In case the console was overheating, I turned it off and tried again the following day, and another freeze within 5 minutes. That's a bit worrying, as I still had the Companions, Thieves Guild questlines to finish, and I'd barely started the Dark Brotherhood, Bards guild and Dawnguard questlines.
So, I tried going back to a older game-file and the freezes have stopped. I also noticed a LOT of stutters when moving about (some fights were barely 1fps), which was fixed simply be dropping out to the Dashboard and re-loading Skyrim. I just installed Dawnguard, so that might have been a factor.