I can't think of a single reason to note defects on bits of paper or in notebooks- the Tech Log is in the flight deck and is probably the easiest thing to enter defects in!
I suspect a lot of us have left stuff out of tech logs to keep an aircraft flying, it is to an extent a judgement call. A good guide to what you should do is imagining yourself explaining your actions to the AAIB at the subsequent board of enquiry.
Part of the problem is the way we use the MEL, which is not really a definitive document and itself requires interpretation.
However, some operators do take liberties and where this affects flight safety, should be jumped on from a great height.