My son has a 4-month-old GSD that snaps or bites often. Should this be acceptable considering his age or should it be corrected?

There are a couple things to consider here:

There is a difference between snapping and chewing. If a pup snaps, this is a way that it warns the person to stop doing what they are doing and leave him alone. Often when this happens the hair will be up on the back and the pup will be showing some teeth in the form of a snarl. This is a concern. I would be very concerned about the temperament on a pup that is doing this. My feeling is that this dog does not belong in the family. In fact it should probably be put to sleep. This behavior is only going to get worse and as an adult it will be a very dangerous animal. These are the dogs that grow up to be fear biters.

Pups from working bloodlines are very mouthy as pups. This is a totally different situation. These pups naturally grab and chew on things. While this can be annoying it is not a sign of a poor temperament. It is no different than a lab pup that is always chasing a toy or chewing on a toy. This mouthiness goes away at 4 1/2 to 5 months of age.
How a person deals with this depends on your goals for the dog. If your child is very young (a baby), the pup needs to be corrected for chewing on the child. Grab it by the nape of the neck and shake it until it screams when it even goes near the baby. If the child is a little older and this chewing is annoying, try and keep several toys around and divert the pup to one of the favorite toys (a tennis ball on a string works well, a rolled up hand towel works well). Just leave these laying around everywhere. If you play enough with the toys and the pup, the toys become more interesting than your hands and pants. Make the toys his center of attention.

The bottom line is that this behavior will go away. In fact this is what I want to see in my pups that are bred for personal protection. If you want to learn more about this, I recommend that you get my video titled Your Puppy 8 Weeks to 8 Months.