I'm working on a large website that has hundreds of pages with headers, footers, pop-ups w/ iframes, buttons, logos, etc all over it.
It's been developed for several years. The entire time there have been no DOCTYPE tags, so all the code that has been written for it has been written against quirks mode.
Here is my question: What are the likely issues to run into if switching the whole thing to non-quirks mode? Are there going to be so many issues that it isn't worth it to switch?
You should go and try it. Make a test installation and test it.
I did the same thing lately and there were some problems. Most of time I had no big problems, but sometimes it is really very hard to fix everything, because standard mode simply doesn't support some weird behaviour of qwirks mode. But I am happy to have the conversion done. Also those pages didn't look the same in all browsers, because qwirks isn't 100% same everywhere.