Browser compatability is becomeing more of an issue, not less of one. In particluar accessibilty for the various degrees of disabled web users is very much at the fore and most web designers are frantically trying to keep pace with the evolving standards and legalities.
Dreamweaver translates layers into CSS positioning, after a fashion. The touble with that is not all browsers support or can cope with absolute positioning and Dreamweaver does not support all browsers in the code it generates.
If you want relaible tables you should avoid multiple nested tables and use the drawing tools to establish your desired row/column/cell attributes.
On its own a <div> tag is a content block, or a container for content, if you prefer. Overlaps can be desirable in some cases, likle where a portion of a page in a corner is used for some menu links and the rest of the page is for content, but controlling them can rapidly get out of hand.
My own opinion is that browsers are, in general, lousy at dealing with a lot of quite common page elements and prefer to attract users based on bells and whistles functions rather than reliable page rendering.
Version 3 browsers are out of the picture as far as I am concerned. I refuse to design to cater for them since in doing so you sacrifice a huge amount of control over your end product and version 4 browsers have been around for longer than anyone cares to remember. Web stats suggest a very high proprtion of users are on the latest version of IE and certainly the majority are on 5.5 or over.
I think it is far more important to design something that can be easily read by text based browsers and screenreader software than something that a version 3 browser can handle.
My own web stats have not shown a version 3 browser for a long time now, and only a small few version 4 browser hits have appeared this last year or so.