Ok, I promised to explain in more detail how to get rid of memory leaks once you've found them. Though I haven't had time to gather all of the information and examples I would have liked, I have run across a few external resources that might be of help.
The first of these is a new Microsoft Technical Article that discusses the various forms that IE memory leaks can take in some detail. Particularly interesting is the fact that it discusses an even more obscure type of leak that's not even a DOM element. It's definitely worth a read.
For a nice, straightforward library that does an excellent job helping you avoid the problem altogether, take a look at Mark Wubben's Event Cache. I particularly like the fact that if you follow a simple set of rules, then you cannot easily leak elements.
On Another Note
I suggested earlier that the slowdown associated with leaking large amounts of memory in IE might be associated with hash tables or something similar getting full and therefore more inefficient. Eric Lippert left the following comment, which makes perfect sense to me and seems more likely to characterize the problem:
The symbol tables are very search-efficient. What's more likely is that the non-generational mark and sweep garbage collector is getting more and more full, and therefore taking longer and longer to walk each time a collection happens. A generational GC, like the .NET framework's GC, solves this problem by not GCing long-lived networks of objects very often.
And don't worry, I haven't forgotten about Drip at all. As time allows, I will be adding the features that I mentioned earlier. Of course, if anyone else wants to play with the source and make their own additions, please feel free!