I am wondering if I have a baby with my 3rd cousin, could there be any problems. I don't even know if he is even really related to me. He is my grandfathers brothers grandson. My mom says he is but I don't see how because my grandfather is her dad & his bro would be her uncle not mine. & then his daughter is my moms 1st cousin and her son is my moms 2nd cousin. So in turn hed be my 3rd cousin. I don't care what other have to say about what I choose to do with my life, my main question is if I have a baby with a 3rd cousin will there be any defects or problems. Etc.

First of all he is your mum's 1st cousin once removed and your second cousin (see What's a Second Cousin vs. a First Cousin Once-Removed? | LiveScience) and since you both share a set of great-grandparents you are definitely related to him.

Secondly, you don't need to be related for your baby to have problems/defects as the majority of babies in the world with problems/defects are born to parents that are not related to each other. Being related just increases the chance of there being problems or defects.

Brothers and sisters share on average half their genes, 1st cousins share a quarter and 2nd cousins share an eighth, so unless there is a history (on your shared great-grandparents side) of possible problems/defects then it is not very likely that your baby will have problems/defects.

Speaking from experience, my parents are 2nd cousins and none of us (4 sisters and 2 brothers) have any problems/defects (that can attributed to our parents being related!).