If I were to rank the common draft mistakes I see among new players, it would be:
1) Not drafting enough creatures. Even small dorky creatures are better than "destroy target artifact" 90% of the time.
2) Not prioritizing removal spells. If the card can kill a creature, you should take it early.
3) Not considering colors. You want your final deck to only have two colors in it if at all possible, so don't spend the first pack just grabbing cards that look sweet. Once you get about halfway through the first pack, take mental stock of the colors you've been taking and try to figure out what your two colors are going to be. From that point, try to only take cards of that color if you can. This isn't a foolproof way to draft, but if you've never drafted before, you're more likely to end up with 23 playable cards if you make this your focus.
That being said, when you open a pack and there's a sweet rare you really want for your collection, don't feel bad about taking it. You can be disciplined about taking the right card for your deck starting with the second pick.