This is most likely a user configuration issue. While auto-minify might work for some people, if you're running many plugins and/or lots of JS files that are potentially written improperly, you could possibly break something leading to problems with the site loading properly.
To alleviate this try switching to minify to manual and using the Help function to "help" find all of your JS and CSS files. Add all of them, making sure to take care in deciding where to add the JS files and what blocking to use. If you're unsure try adding them to the section (head or end of body) that they are already located at in your code and use blocking.
For the first round of testing do not use any of the advanced check boxes for the JS settings.
If after adding all of the JS files and CSS without any advanced features you can try to enable comment removal and line space removal if you like.
If either of these rounds of settings breaks your site, try only adding one JS file at a time. Once one JS file has been added and you have tested it on your site add another and test again. Do this until you find the file(s) that are not working when minified. You can then try to run them through JSlint to find errors or contact whoever developed the files to help with fixing them. If you are unable to fix a file that is not working while minified then don't minify that file. You can select as few or as many files to combine and minify as you like.
W3TC is an advanced plugin that requires time, experience, and tweaking in order to use it properly. I am personally running the development plugin on WP 3.1 Multi-site with about 10 sites. It works fantastically with no major issues.