Am I correct that you're using the built-in browser?
If so, I'd try another browser. I'm still experimenting with the alternatives, but I've had a lot of problems with the stock browser.
You're touching the X on the tab and the tab doesn't close? I thought I had that happen the first time I used the stock browser -- except that I had accidentally opened a slew of Google search tabs, and they were closing. It just took a while to get enough closed so there were few enough tabs that I could see the end of them and watch the tabs I was closing drop off.
To close the browser, close all the tabs but the last one (you have to have one tab), then use the back button to close the browser itself.
Never any need to reboot the tablet. If you have an app that won't close, go to
Settings>Applications>Manage Applications>Application that's not closing>select "Force Close"