Is there anything wrong with dating or marrying a third cousin? If you don't care that people know you are third cousins, or don't advertise that fact to non-family members, there will be no moral judgment.
I would like to know the legallity and moral standpoints as far as the law is concerned. The morality of it, is a very personal issue and different people would have different views on the subject.
From a moral standpoint, dating only, of course, is much different from marrying a third cousin, but it could lead to marriage, so I understand you why you're asking this.
To understand the legal ramifications, you would need to contact an attorney in your State who could let you know if there are any laws on the books prohibiting this; the rules vary from State to State, but some laws are very old and antequated.
Short answer: sure, unless your family has a history of genetic problems.