Hrm. I've found Mozilla builds to be more stable than Netscape 7.x. I don't grab nightly builds, but read the changelog before getting a new version. Other than more frequent refreshes, I don't like some of the things that AOL/Netscape's package comes with. They may have changed things though - it's been a while since I got a new Netscape version.
I use Mozilla as my default browser, with IE 6 as a backup for certain situations. I don't use plugins in Mozilla, so if I need to view some Flash or Director material, or streaming media, I'll fire up IE. You can drag URL's or links from Mozilla and drop into IE's window. I wish that Mozilla had IE's cookie handling - there are a small number of sites from which I will accept cookies so it's easier to define those manually and block everything else (IE) than to constantly deal with confirmation popups or turn cookies off (Mozilla). Keeping a list of cookies to block is far less efficient than keeping a short list of cookies to accept.
I seldom come across rendering problems in Mozilla, but when I do I can simply drop into IE. More often I automatically ignore a site that is poorly coded enough not to render in Moz. Sometimes it is not bad coding but use of ActiveX controls or IE-specific features. I ignore those sites as well, for my own philosophical reasons.
If you use extra toolbar features (Google bar, etc) in IE then you might miss those. There are sidebars for many sites, but they are generally not as robust as IE toolbars.
I find that Mozilla's options for controlling ads and unrequested content work far better, in conjunction with my firewall, than does IE.
It will be interesting to see the next major iteration of Mozilla. The stated goal is to separate the browser from the email and newsgroup component, reduce code bloat, and improve speed. Hopefully this will take less time than it took to get to Mozilla 1.0
All that said, I'm pretty happy with Mozilla. When I run into things that I don't like, I can often do a bit of Googling for answers and mod some Mozilla configuration files to change the behaviour. This is less often the case with IE.