Factual error: When you are facing Lance in the champion room, he uses three Dragonites in the battle. Two of them are at level 47, and the other one is level 50. However, Dragonair only becomes Dragonite at level 55.
Factual error: When you reach the champion in Pokemon Gold, you have to defeat his Pokemon. His 4th one, Aerodactyl, knows the move Rock Slide. Aerodactyl cannot learn this move, and it does not appear as a TM in this generation.
Plot hole: At the Ruins of Alph, when you solve your first stone puzzle, you fall down to the ruins, where there is a "strange presence". Now, you can encounter Unown, a Pokemon. After this, you tell the scientists nearby about them, and help them solve the puzzle. However, if you make it out of the Ruins without seeing any Pokemon, talk to the scientists and they still know about them, even though you haven't seen them.
Plot hole: Near the beginning of the game, you tell a policeman the name of a boy who has stolen a Pokemon. If you click 'end' straight away, the officer will say 'OK, so SILVER was his name'. Even though this is a default setting of the game that is chosen when you press 'END', there is nothing in the story to explain how he knows the name of the boy.
Continuity mistake: When going into a Pokémon Center with five Pokémon and one egg, when healing the Pokémon, six Poké Balls will show up on the machine. How can there be six if one's an egg?
