My personal pet peeve is when they play an ad before giving you the menu options.
First, wait thirty seconds for them to tell me how great their mobile app is. Then listen to the options, pick one, find out I picked the wrong one, and have to go back up one level. Now I have to listen to the ad again before I can hear the options.
I don't care how proud you are of your app, I wouldn't be calling you if I could solve my problem with it.
Bit of an obscure one, but Fire Emblem Gaiden.
There is a miniscule (0.014%) chance for the very first enemies in the game to drop an extremely powerful item that normally isn't available until much later. Getting it early is absolutely wild because one of its effects is doubling stat gains when leveling up, which can quickly snowball your characters into godhood.