First of all, this sounds like attempted preferential verification, which is pretty frowned upon in most situations. The one case that it could be useful for, like you said, is rejected runs, but then again it's pretty easy to scroll through the list and take quick glances at the rejection notes.

[quote=VyPr]this sounds like attempted preferential verification, which is pretty frowned upon[/quote]

It's not just frowned-upon, it's not allowed at all. [quote=Site Moderation Rules] • Preferential treatment of any type (moving runs up in the verification queue, verifying runs that do not meet standards, etc) is forbidden, especially if associated with payment or favors. Failure to remain impartial may result in moderator removal. [/quote]

That said. Wanting to able to search does not necessarily imply preferential treatment. If you got halfway through verifying a run and came back to it later it might be helpful to just search for it directly rather than sifting through the whole list. Or if you watched a run live/otherwise before it was submitted, etc. Though I think very few games actually have so many pending runs at any given time that this is a major concern, and the first situation would be solved more easily by just being able to assign runs to specific moderators, and then having something that just shows your assigned runs (I think this is a planned feature, if not it definitely should be).