Are you allowing anonymous checkout? Are all of these screwy orders coming from anonymous customers? You might try disabling the anonymous config ... see if that helps.

So, if you go into the uc_orders table in your database, you are seeing orders that you didn't create that are given a uid of 1? (In other words are associating with your account at the db level)

I've heard of something like this happening - I think when our site first went live, we were getting users whose orders were tripping over each other or overwriting a previous order. I think Lyle had mentioned something about it being a PHP but, but for the life of me I can't remember - nor can I find it in my posting history. It's like the sessions are being cached or something - and a user is coming to your site and checking out but somehow their session information is being overwritten by yours.

What versions of PHP and Apache are you on? Or are you on Windows?