My uncle (my mum's brother) married his first cousin. They were born in the 1920s, married in 1953 and had a son in 1964. My cousin (their son) seems fine. Also, I have been researching my family tree, and found two first cousins who married each other (in the 1890s).
I think it is more likely to be a problem if there is a lot of marrying of close relations in a family, but if it is a one-off, then I shouldn't think the risks are that great.
I should add that my uncle had a great many (non-related) girlfriends before he settled down with his cousin!