Continuity mistake: In every gym there is a statue that lists the names of all the people who have won there. The only names that appear are the player character's and their rival's, but when you go to the elite four there are all these other trainers. How did they get past the guards when they don't have any badges?
Continuity mistake: If you come to Pallet from the south, that is, surfing, you can see that the fat man near the lab will appear out of nowhere when you enter the town.