I'd love it if saved searches could have relative dates, e.g. "2 months ago", "1 week ago", etc. In bugzilla the format is "2m", "2w", "2d", "2h". (I'm not sure if we'd want years, also.)
We're also updating this control a bit in connection with work on Calendar, so I think it will look like this soon:
Start Date: [___2014/05/01] [#] [12:34] ^ | +-- Date Picker
When that does happen, you can still type "3 months ago" into the left-hand box and it will work the same way, we're just trying to make it easier to use normal dates as well.