My personal "annoying" moment was the Snorlax blocking the entrance to Diglett Cave. How in the world was I supposed to know that I had to tune in to the Poké Flute channel made just for this purpose and then press A on the sleeping giant? I was sidelined for a good couple of weeks...curse you for not being present in my house at the time, internet.
Also, I think this also counts as annoying, although I think it's kind of unfair to say that a vastly watered-down Kanto could be considered "annoying" when we should just be glad enough that Game Freak let us go back there in any capacity.
But, it really is the only thing that makes me feel kind of bad about the game (otherwise it's Gold-en!). No Safari Zone, pint-sized versions of maps (Viridian Forest, Mt. Moon, Victory Road), missing Kanto tunes, disappointing battle remixes, and an "excused" lack of Cinnabar Island...all of those things eventually leave the player with a feeling of "they could have tried harder." Yeah, I know the Safari Zone and Cinnabar would have properly in the game given more time, but still, they could have tried harder!