Most of the time these mistakes are small. They won't break the game or send your group running for the hills. But everyone wants their first time to go well, and the more mistakes you can avoid the better it will be for everybody.
1. Read, Read, Read
It happens to every GM. At some point, you forget a monster rule that totally messes up a fight, or you misunderstand part of the adventure module you are running and cause problems for yourself down the line, or at the very least you forget a rule and have to stop the game and go flipping through a bunch of books trying to find it.
This may seem obvious, but the hands-down best way you can prepare for your first stint as a GM is to read all the material cover-to-cover beforehand. Read the main rulebooks for the system you are using. If you are running a pre-made adventure, read the module all the way through. Before a fight, read the monster stat blocks to make sure you understand everything it can do. Even if you've read the rulebooks before, back when you were a player, read them again. You pick up on different things when you are reading them to learn how to play than when you are reading them to learn how to GM. You might even find that your regular GM has been misinterpreting a crucial rule!
Not only is this great preparation work, but it is also a good way to come up with new ideas. You might come across a set of rules that doesn't get used much in your group and decide to build an encounter around it. When I was reading through the 3rd Edition Dungeon Master's Guide while preparing for my first time as a GM, I got really inspired by the section on fire and heat hazards and decided to add a house fire into the scenario. The result was an exciting non-combat encounter that gave a new player an opportunity to feel like a hero.