Actually getting a bike. My brother kept telling me it was easy, but I could never figure out how. X,x; I always got him to do it instead.
Caves with Zubats, Hikers with Geodudes/Onix, etc. I really hated the cave to Lavender Town. I would use flash, but it still annoyed me. I got mad one time because once you leave the cave, there's like three or four trainers on the way to Lavender Town. All of my Pokémon would be really beat up. It was hard for my 8-year-old mind to avoid trainers. xD
Silph. Co.
When hard to catch Safari Zone Pokémon such as Chansey and Kangaskhan run away. >,<
Fighting Brock when my strongest Pokémon was Pikachu.
Having to go through the Cinnabar Island Mansion. My younger mind never understood why a key is buried in an abandoned mansion that unlocks a building close to it.