eg UK such as female Spanish Sparrow obviously not overlooked in their home range.
Probably not even looked at in their territory....
So
1. Overlooked to me is something that is missed because it blends in with the crowd or through lack of knowledge...
A strange Pipit race or juv gull in a flock of thousands. How times have we found something that is 'different' from the rest of the flock but we can't put our finger on it? Pre-digital cameras, pre-colour field guides - Collins? Not much chance. Already had the Slaty Gull reference.
Can you remember the difficulty pre cd's in winding through an old tape recorder to try and pinpoint a call?
Another bird not, knowingly, seen by me would be Pacific Diver (although 99.9999999% sure haven't). How many would have been overlooked over time - considering it has got to have been fairly regular west coast bird after big storms? Once you find one you find more - 50 years ago who would be looking for one?
Nowadays you get a digital camera snap, you tape a bird out with your mobile phone, within 15 minutes other birders are on site to verify something. In the 'olden' days you see a bird its gone and then going home and phoning someone to say you might have seen something but it was quick so you're not sure and you might have or not got a snap which you will wait for the end of the film before processing
Once you've heard a Yellow Browed or such like you find more and more...
2. Not found is not found because of its habits or habitat.
Nocturnal birds, birds in the middle of reeds, buried in Woodland or in very loosely watched areas...
One example is the Aquatic Warbler in South West France - 10 or so records over the years then a change in ringing method produced 40 birds in two weeks one August. Something about the nets being placed parallel to the ditches about a metre away and closer to the ground which completely changed the capture rate.
Another would be Wallcreeper - when we changed our prospection period, to earlier, and area to lower we immediately started finding nests - we have a Swiss birder to thank for a Wallcreeper paper he did on his local birds. And finally the Eagle Owls - historically birders were looking too high. An adjustment bought immediate results - there is an interesting paper on the subject I might dig out...