Hello,
My question. If a merchant runs your credit card through with the wrong amount, and you sign the slip. Once you leave the store they run your card through again with the additional amount. Are they allow to do that? When they have no signature on the second slip. Is that a charge that I can dispute. It's not my fault if they charged me less.

You can definitely dispute that charge. Just call your credit card issuer and they will research the problem for you.