I have gotten pretty far along in the game, and pretty far along in a certain city, with everything working perfectly. Now suddenly all of the people in buildings who move around to let you know they are functional have frozen. The rest of the city moves perfectly; people walk down the street just the same and it's business as usual. Just the figures in buildings are still. If I build a new building, it will show that it is staffed and operational but no figure will appear in it. The city looks dead! Anyone had this problem?

What type of buildings are we talking about? Like industry type buildings? A lot of those require resources, and if memory serves you won't see people in the building until they have something to do. Eg, a papyrus maker could be fully staffed and operational but show no activity at all, but the moment some reeds get delivered to the building it becomes animated with a guy(s) turning the reeds into papyrus. I think that the animation can also stop if the warehouses if nobody comes to collect the accumulated commodity created by the industry. That is, the papyrus maker building is only active with an animation as long as it has a supply of reeds and the papyrus that it creates is taken to a warehouse.

This bug is common for people. You can try restarting your computer to see if that clears it up. I can't remember the fixes that were stated for this, but I do know restarting is the #1 fix for most of the bugs caused.

But of course, it could also be as a result of what the user above me suggested: your buildings don't have the required raw materials to operate.