I am finishing my basement. I recently found out that I need a building permit. What happens when I get the permit and the inspector comes out.

You should get a permit and get the basement inspected sooner than later.  It will only get more expensive after the basement is finished. An inspector will come out and you will have to prove that the improvements have been made to code.  If you do't do this you will have a problem when you are ready to sell the property.     Good Luck.