Nack wrote:
My current practice is that after finding the key, I'm never satisfied until I've seen why every other possible move doesn't work. Good problems typically contain at least a few clever defenses.
Yes. Often, in modern problems, you'll see a stipulation like "#2✓✓✓" where "#2" means "White to move and mate in 2" and the three checkmarks indicate three "tries" (plausible moves that are refuted by a unique defense). In the #2✓✓✓✓ problem below (A. C. Reeves, Probleembad, 1965), you would miss most of the beauty of the composition if you stopped after finding the correct key move, and didn't look for the tries.
The key(s) in twin problems are relatively unsubtle compared to most good chess compositions.
That is usually true, and it is perhaps one reason that twins are not so popular in standard ("directmate") problems (though they are popular in helpmates). But while looking for some examples, I ran across a blog post by Kabe Moen with some excellent examples of twins. I found the two problems by Marjan Kovacevic particularly pleasing.