I've missed much worse things than hanging pawns :)
Honestly, the whole "staying in the moment thing" is something I've only started to appreciate recently. I might calculate beautifully some tricky 5 move line, and even evaluate the position afterwards, yet I might still miss some one-move pin trick or fork every now and then. Maybe when you calculate tricky lines it makes you assume you will automatically see the one or two move stuff, and so you stop doing what you always do to make sure you don't make those mistakes; you let your guard down.
So yeah, perhaps I should try to incorporate some time during thinking where I simply ask myself, am I making this more complicated than it is? Is there a much simpler, back to basics idea/tactic here I'm taking for granted? Only problem with that is that these situations happen because I'm not thinking this way, and if I'm not thinking that way I'll never do this check :) But ok, I can get some practice doing this so that I'm more used to it.
Because yeah, it's worth pointing out that masters, etc., don't necessarily catch the mistakes of lower-rateds in complicated variations -- a lot of times the lower rated player eventually gets too distracted under pressure and misses something relatively simple. In other words they can't keep a healthy state of mind for as long as the master player.
Definitely agree with seeiming the position anew. Plenty of times I've gotten so caught up in what my winning plan was that I missed easier wins. I start getting into a "the tactics are over, I just have to bring this home for a simple win" mindset which hinders me.
I wouldn't put missing a mate in 3 for a mate in 5 in the same category though. :)