My mom watches my 6 month old son. Recently she was diagnosed with croup. Should I be worried and have my son checked out? He has a slight cough.

Yes. The viruses that can cause a "croup" infection are very contagious - especially to children.
Odd diagnosis. Croup is a label applied to a symptomatic infection of the airway in kids 6 mo to 6 yrs of age with a specific pattern of symptoms.I have seen it as old as 8, but have never seen the term used for anyone older, particularly an adult. I wouldn't look to the kids slight cough any more than any other time.Monitor and call in to the doc if you are concerned.
Maybe. If your son is acting sick then he should be see. Watch http://www.Youtube.Com/watch?V=bf5sxehpgck to learn more about croup.