Calendar:
From the user side it all looks decent, if only a little slow to display/hide an event. I imagine something so large though wouldn't have much use in your average web site? Generally you see a small (say 300px by 200px) little calendar on the home page or something. Can this condense at all? One more thing is the ability to link another person to an event / month or something; this could also be tied in with none-JS support.
The admin side of it it's a little basic in comparison. Why does it tell me at the side of each input the default value, instead of actually just making that the default value? Why is there no "preview" link, or at least link back to the calendar for checking an added event?
Chat room:
Not much to critique. Functionality wise it all seems to work - though I'd say it's lacking in features. The design's very basic but I assume this just to be a kind of prototype?