Ideally, I'd like the current product field to just be a bit of text, with a "move..." button/link next to it. That should use JS to open a dialog which lets me search for components the way I do on enter_bug.cgi (with the autocomplete widget... not sure what that's called), or alternatively, one that loads the product's set of components and versions using XHR, so I can set everything on the same page. This would save me oodles of time when moving stuff in triage, nevermind the fact that the current intermediate screen ("you need to pick a component and version") has bugs (sometimes it autoselects a version, sometimes it doesn't) and has no context (I can't read the bug while I'm on this screen, so when I then have to think back "did this user report for Seamonkey 2.33 or 2.32?" I have to go back a page, doublecheck, and then click the 'save' button again to come back to the screen with the right version info in my brain).

this is really bug 227611. unfortunately changing the product has more moving parts than just the component - there are quite a few other fields whose fields are per-component (versions, milestones, custom fields) making this more complicated than you'd initially think to fix. (fwiw i'd love to see this fixed too!)