I completed my sons taxes, and stated that someone could claim him as a dependant. I am doing mine, I can not claim him as a dependant. Will this effect his tax refund?

No, but if you cannot claim him as a dependent, depending on his situation, you may want to amend his return as he could possibly be eligible for credits he wasn't eligible for when you were claiming him such as educational credits or depending on age and income, Earned Income Credit.

If he is not, then you not claiming him will not affect anything.