1. The top navigation. Whenever I zoom in or out, it looks terrible. Is there anything I can do to keep the links in place with the background image?
Yes, set the background image on the individual elements rather than the #nav div - then the background will shrink or expand with the text. Have a look at this sliding doors technique
(it's an oldy but goody) which would work well for your tabs.
.....How can I go about doing this? Would tables be best to use, or just separate div's and classes? My guess is that I'll probably have to make the site wider in order to fit them in side by side
Don't even think about using tables - it's inflexible and unnecessary!!! Divs would be fine, float the divs and they'll then just stack up next to each other.
Other options - have a set of quicklinks at the top to facilitate quick navigation, if you want to get a bit more flash have the details of the products in an expanding/collpasing div so the page isn't so long (have a look at using jQuery for this maybe .slideDown() - you've already got it on the page).
3. I really feel like the site is lacking of something but I just don't know what.
Seen a lot worse to be honest.
Not keen on the scrollbar in the news div - have less, or maybe scroll it automatically?
Not madly keen on the two blue squares on the side nav, combined with the font in use.
Also, it took me some time to realise that the two menus are (almost?) the same - I think this is potentially confusing. It made me think - and that's usually bad for websites (see the classic Don't Make Me Think
by Steve Krug - another oldy but essential reading in my opinion.
Design wise, blue background is a little dull but I can't get worked up. I like the top image. Having the whole page wider would have more of an impact - but I have a widescreen and it's fine
Picky picky picky but your favicon looks a bit pixellated.
Text on the images "Ion Exchange Resins" doesn't look very smooth either - you could just overlay real text on the image rather than including it in the image.
Hope that's helpful....