Something that plagues low-level D&D is the swinginess of combat due to the d20 attack roll. A handful of exceptionally poor rolls can easily turn an encounter from a cakewalk to a slaughterhouse (or vice-versa). I'm fine with some degree of swinginess--it helps build tension, after all--but I find that low-level D&D is too swingy for my tastes.
You can also consider changing your dice.
As we all know, the d20 will give you a 1 just as often as a 20. At low levels, when your bonuses to anything tend to be smaller, the character matters far, far less than the roll of the die itself. You're at the mercy of the dice. It's a little frustrating.
You may want to consider using 2d10 or 3d6 instead. These both help produce more average results. My guys prefer the 2d10 because it still allows for natural 20s (and what is more D&D than a natural 20?), but I think 3d6 could work just as well (if not better).
Average roll on a d20 is 10.5; average roll on 2d10 is 11; average roll on 3d6 is 10.5. But, the 2d10 / 3d6 are far more likely to produce numbers in the middle, and very high or low rolls become more rare.
The result is that things are a little more predictable; if you run the numbers on a specific combat scenario you can be reasonably assured that things will end up the way you modeled them. It also helps the players as well. They can depend more on their skill / attribute bonuses more than praying that the dice won't screw them 5% of the time.
If you go this route, you should consider altering critical threat ranges for certain weapons as well. Not only are higher numbers more scarce, but in the case of 3d6, you can't roll a 19 or 20 (or a 1 or a 2 - we rule that rolling all 1s is an auto-miss).
Aside from fiddling with critical threat ranges on weapons, we haven't had to change anything else so far.
An idea I've toyed with is allowing the player to choose which dice to roll whenever he does something. If he's reasonably confident that his character can perform a task given an average result, roll the 2d10. If he really needs that 19 or 20, he can pray to lady luck and roll the d20 instead - which also carries a greater risk of a 1 or 2.