I've discovered some glitches in Red that I never knew could happen.
You probably know that you can fish "inside" pillars/statues at Fuschia Gym, right? Well, you can also fish inside the ones at the Cerulean Gym, but here's the thing: you can catch Pokemon! I didn't know that you could fish in any statue, and even strategy guides said that nothing can be caught in the FG's statues, but I fished out a Lvl. 15 Psyduck in the CG.
Also, inside the Unknown Dungeon, where you catch Mewtwo, there are the raised platforms/hills that you normally can't stand on. Well, on the route to (refer to spoiler), immediatelly when you exit the 2nd ladder on the only right route, go down, and you will be standing on the platform! However, the only ay to get off is to go back down the ladder. Also, when your only a few steps away from (refer to spoiler), there is a bigger platform. Go to the shaded side that appears to be not as steep as the other side, and you can step up/on that platform, too! You can also face Pokemon there. If I can, I will get pictures.