I believe there are no more problem with these two specific events than with all events in Internet Explorer plus the usual weird quirks such as this one.
The general solution to event-handling and MANY other problems is to use a Javascript framework whose developers have bled their own blood to save yours, papering over all IE (and a few other) weirdnesses, such as dojo. As the Dojo folks say on that page:
The word "support" means something
very specific for Dojo and Dijit, in
that saying that Dojo Core and Dijit
support a browser means that 100% of
the available functionality works,
that accessibility is handled
correctly, and that all
internationalization and localization
is supported. This is a very high
bar, which also means that while we
may not saying that browsers like
Opera are "supported" for Dijit, it's
highly likely that it will all work
there too, but there may be some
caveat which we were not able to work
around (such as accessibility hook on
Opera).
The browsers they claim as "supported" at this very-high-bar level are (as of Dojo 1.3.2) IE 6 to 8, Safari 3.1 to 4, Firefox 2 to 3.5, Chrome 1 to 2 (core functionality, including event handling, also works on Opera, Konqueror, FF 1.5, ...).