Can a credit card company garnesh a joint checking account for a debt that is in one of the account holders? Note the joint account is in a father/son situation. Father has debt collection against him and son is innocent party.

Yes they can. A joint account can be garnished as easily as a single account holder account can. Just because one party is "innocent" means nothing. In a joint account the money is either all one parties' money or all the other parties' money meaning that either party can withdraw the entire amount out of the account at any time.