We’ve been working on these Sunday Times puzzles together nearly every weekend for the past 20 years. One thing we’ve noticed is if you get stuck and put it down part-way through, when you resume it feels as if your brain has been quietly working on it in the background - many of the stumpers become obvious.
Rex Parker (self proclaimed - Greatest crossword puzzle solver in the Universe) is often how we check our work. He has a humorous blog that critiques every puzzle - some so harshly, it seems he may need therapy.
See his thorough analysis here.