I am looking to buy this accessory for the Gamecube. However, I read on some internet forums that some GBA games like Castlevania Double Pack don't run properly. Is this a generalized error or something anecdotal? Because I was thinking on buying it in order to play the exact same game on my system.
It seems that all officially licensed original Game Boy games, Game Boy Color games, GBA games, and the eReader should work with the Gameboy player.
This post indicates the contrary. Perhaps the forum poster you mentioned had a bootleg copy?
While games will works some games with extras such as the tilt sensor (Kirby Tilt ‘n’ Tumble comes to mind) or rumble pak might have issues as they were never designed to be used with the Gameboy Player on the Gamecube.
It's a bit cumbersome to use the tilt sensor as you'll have to hold play with holding the Gamecube system's handle in order to get it to work and can be quite taxing on your wrist and the system's handle (don't drop it!) as the Gamecube is simply too heavy to tilt, flip, and hold flat with one hand, while holding the controller in the other.
The rumble pak doesn't have any effect on the GC controller and will just vibrate your GC system, so it's somewhat pointless.
Some games might scale better than others onto a TV screen. You might notice some blurriness or certain games like Pokemon Sapphire/Ruby, but nothing that would affect the gameplay.