One usually has to find a spot in the music where there is a strong attack for an analog edit to be inaudible. It also helps to have skilled musicians who can accurately recreate the tempos and dynamics so the music doesn't suddenly slow down or lunge ahead at the edit points! I usually used headphones so I could hear every little detail while editing.
Yes. I actually do a large amount of audio editing in the digital domain and also use headphones. That said, I am usually not stitching takes together (though I do that too) and am usually repairing a raw vinyl transcription. However whenever I create an edit point, I will test it with the headphones used in both "normal" listening mode and then also with Dolby Headphone enabled. The reason for that is because if I only use the headphones normally, I've found I can miss certain "phasey" effects that are sometimes introduced by the editing algorithms that suddenly become very obvious when listening via speakers, but are inaudible when listening via headphone (that works both ways too - things inaudible on speakers but audible with headphones). But I know I am perfectly happy with an edit when it is completely inaudible when listening with headphones in both listening "modes", since the Dolby Headphone re-creates the same sort of listening perspective and "phasiness" (if there is such a word) of speakers.