Common thread here seems to be repetition, and lots of it.
Also most of us appear to make use of multi-channel (for lack of a better word) methods: writing plus hearing, hearing plus reading, etc.

One thing I might add is that, when I find myself getting stuck at transitions, learning the song back-to-front helps. (Old choral director's trick.)

Normally I'll memorize the first verse (and chorus) thoroughly, then go to the last verse/chorus. Once I can't miss on the last verse, I back up to the next-last one and make sure I get the transition without a hitch, every time. Then the next-preceding one.

It's mostly about training the mind to not get jammed at the seams. Plus it has the advantage that by the time you are done, the part you know best is the ending -- the part that leaves the final impression.

-Glenn