There is no harm IMHO of Captins "carrying" minor snags that don't affect the safty of the aircraft.
Coming from an RAF background, we use 3 systems, the ADH log- Acceptable deferred husbandry, for stuff like fabric patches missing, missing/scratched paint etc.
ADF long- Acceptable deffered faults- minor stuff like only 1 of the two tail lights working/ bulb gone etc etc, anything that is a grievance but has no adverse limitation or operational effects on the A/C.
Lim log- Limitations log, anything that will affect the performance or operation of the aircraft, like a generator that is not working/ 1 of a pair of instruments no working like an ADI for example. Being mil we obviously can take larger faults than civvy airlines, and sometimes operate the aircraft with major faults just to get them back to a safe service centre. But again, the degree of the problem we are allowed to carry is balanced against the risk to the A/C and personel.
I think the system works well, and if used properly is a very safe way of flying with minor snags to prevent the loss of the sortie. All down to the Captin though, if he refuses to fly with any problem it's his/her call and the problem will get fixed before the next flight.