Mold near door? How concerned should I be

I would be aware, but not overly concerned. (Unless you are very sensitive) Use some 100% bleach wipe the area and dry it off well. It could have been a bed sheet closed in the door during rain or maybe a spilled drink. Worse case a bad door seal or door alignment issue.
Once dry, keep an eye on it. 
Check the mattress as well. Make sure it is and stays dry. You could leave the mattress out in the sun (inside at night) for a few days. If it smells after that, then consider replacement.