Not sure if the OP meant actual aborting of a takeoff, or he is talking about what sort of minor issues would cause a flight to be delayed until an issue is resolved.

Assuming it's the latter, even minor mechanical issues can result in flight delays. In one case on UA, it was a door on a galley cart (!). And this is on a flight from HKG-EWR which made an unusual stop in SFO to take on new crew (crew rest issues due to flight delayed by typhoon). So a cart door broke somewhere between HKG and SFO, the extra stop in SFO happened, and then we waited 3 hours for them to find the part to fix. And they couldn't find the part, so then they had to get special dispensation to take off with this issue. Said dispensation took another hour, so the flight already delayed 15 hours, plus extended by 3 hours to make an extra stop, now was delayed another 4 hours.
I've seen a broken light on the exit path lighting delay a flight (probably not a bad idea, it's safety equipment) but also far more minor issues such as a broken coffee machine. I always thought the right thing to do is for the captain to say "folks ... we have a broken coffee machine. Should we wait to fix or take off with only 3 working coffee machines." I would imagine the vote would come in positive, and then anyone disagreeing could deplane an take a later flight.
A flight in India where a mouse was running around the plane -- they had to deplane everyone, catch the mouse, and disinfect the plane.
Toilet issues are fairly common causes of flight delays.