Hi jasjen1, you're doing some good work on the sites. I like the sitename you put on the nav buttons, it's a nice customization while still subtle. Please make sure that you have updated to the current stable release of Joomla, which is 1.0.11. There were some date issues with previous versions, as well as some fairly well-known vulnerabilites that an upgrade will patch.
If that's not a problem, then configuration is probably the next thing to look at. There are 2 different time modifiers in the admin section: "Time Offset" and "Server Offset" which can be maintained through the Global settings or directly in the configuration.php file.
It's probably weird seeing the dates being different from a value you directly typed in, but they're stored in GMT. Most likely the suspect components are only paying attention to one of the offset values when calculating local time. Sounds like this problem only happens with the calendar, so changing the offsets probably isn't enough to fix it. If you're comfortable with php this is a good opportunity to peek inside the calendar module. If not, I'd be happy to take a quick look if you wanted to hook me up with a copy of the file.