In my experience.....(no particular order!)
As maintenance engineer-. .1. Seeping hydraulic leaks (at least a couple on any aircraft if you look hard enough!). .2. Broken bonding leads. .3. Chaffing pipework (often a result of perished "p" clip rubber). .4. Corroded panel screws that require to be drilled out. .5. Damaged tyre tread
As a flight engineer-. .Electrical problems mainly. GCB's that keep tripping out, CSD disconnects, transducer problems eg loss of an EPR indication, various lights. etc.etc....