What types of issues are you having? Other than suspiciously small font sizes which might annoy some users, everything looks to be in order.
Digging into your code, things don't look too out of whack. You have some opportunities to significantly reduce the amount of code there by using some shorthand techniques and declaring anchor styles without pseudo-classes. I'd also make certain you declared a color to go with every background and vice versa and I'd move your font family into the body, thereby declaring it only once.
BTW, I'm viewing your site on Opera 7.23 (there were no major changes to standards support between this version and 7.5), and again, everything's pretty much good. So again, what are you seeing that has you concerned in certain browsers?
Ok, right off the bat, it looks like he started a new table row inside of a <td> without declaring a new table or closing out the old row. This is probably causing the erratic placement of logo and text. I would start by running this through a validator, just to clean up the obvious errors (there are many, sorry). HTML Help provides perhaps the best one around. You can do a quick CSS check here as well. It won't point out ways to code more efficiently, but at least it will warn you about errors.
However, the design you've got here can be simplified significantly. In fact, I'd be willing to say you could cut the code that makes up the page's structure by 75% with a little thought. The validator is a good start though. Good luck!