When downloading files or accepting ActiveX components in a web page, IE forces the page to refresh. This refresh can change the state of the website, which is very annoying and can occasionally, result in an endless loop, never allowing you to get what you need done. I've actually had this endless loop problem on MSDN subscriber downloads, which makes it even worse. This instance was because of frames, if that helps.
I believe Firefox has the same refresh requirement, but I'm not sure. Theirs is different, tho. Obviously, they don't use ActiveX, so that's not an issue. Instead, their acceptance comes with installing extensions -- the equivalent to ActiveX controls. When you install a new extension, you have to approve the site you're downloading it from. I can't remember if this forces a complete refresh or if it simply means you have to click the link again. Either way, it's pointless.
I'm assuming that IE handles ActiveX by removing the HTML from the page before displaying it. There has got to be a way to dynamically re-insert this HTML after the ActiveX has been approved. Popups might be a bit harder, because they're all about scripting that's getting blocked. As far as I can think of, there's no way to tell what scripts have run which led to the popup being called. On top of that, attempting to run the scripts again may corrupt the data or cause other data integrity issues. Actually, I guess the scripts can be parsed to determine their meaning, but that would be a major effort and wouldn't even touch on the second issue.
All-in-all, I'm not sure how much can be done about this, but something needs to change. I'd love to take this on as a project, but I think I need to tackle a few other simpler IE extensions, first.