If you build your site correctly with valid HTML and CSS, there is very little cross-browser variation to deal with.
Firefox, Chrome, Safari and Opera are all web standards compliant browsers, so if you're seeing problems in one of those browsers you have a deeper problem that needs fixing.
Start by validating your code with the W3C Code Validation Tools:
HTML - http://validator.w3.org/
IE is and always has been the problem child. If your site is broken in IE, use Conditional Comments.
Hi again Nancy. There's one button that's misbehaving. The others deceived me because in Firefox you have to depress the mouse and not simply click it. However, I just noticed an extenuating circumstance. My browsers are infected by a virus that selects words from text appearing on my website and converts them to links (underlined, with blue text) to advertised products. Maybe there's a connection. Anyway, time for more experimentation. Thanks ever so much for the links for verifying the code.
The problem with the button malfunctioning in Firefox and not IE was actually -if one can believe it- IE not reacting to a discrepancy that Firefox caught. The discrepancy was a rectangular button graphic that had been saved with jpg resolution of 600 ppi whereas the rectangular graphics it replaced (mousedown) had been saved jpg 72 ppi. Once that problem was fixed, it was Firefox that performed perfectly whereas the buttons in IE would only change colors on mouseover and mouseup, and not mousedown. I guess this is what Nancy O meant when she said IE had "always been a problem child".