I've never had the misfortune of an uncatcheable shiny and I've yet to make a serious effort at the battle facilities. Missing my frame when RNGing has hacked me off; recently in Pearl I decided to do most of the advancement by cycling, it takes longer but the Poketch counts the steps so you can't lose count.
So the most frustrating moment...that would be way back when I was a kid and playing Red for the first time, I couldn't get past the Snorlax. I thought you had to push it out the way, it's a big heavy Pokemon and I knew there was a Strength HM, so I searched EVERYWHERE over and over looking for it. Never did it occur to me to wake Snorlax up and in the end I quit the playthrough.
"If I may guess, Emboar might be an exception to the norm that the scalding liquid is expelled from the Pokémon's mouth" - Cobraroll, on Emboar learning Scald.
"Nothing like a cup of tea to start off the day" - Professor Oak, EP025.