I can see the problem seems to be happening on pretty much all pages except the events archive.
The first thing to do would be to just re-save the permalinks and see if that helps.
If not then I would try disabling plugins to see if you can identify one or some combination that is responsible. This doesn't look like a problem that would be caused by Toolset, but try disabling Views/Blocks (used for creating templates and custom archives) or Access (setting visibility permissions; possibly relevant if guests can't see pages but logged-in as an admin you can).