It's by design that the 10 digit number changes, so there won't be any css caching issues since anytime the stylesheet is changed the filename actually changes.
Basically, a user has a "style" preference. This is loaded at run time when a page is generated and tells the scripts what images and stylesheet to use. The only place the stylesheet name is ever loaded from is that "style" file. You'll see them in your styles directory, entitled something like 1.php, 2.php, etc.
The errors are a bit strange. The only thing I can think is that perhaps someone is loading a page at the same time that you're updating the style which might result in that.
Will need to look at the blank.gif problems.
