On what grounds are criminal laws challenged as to whether they meet Constitutional requirements?

Criminal laws can be challenged on a variety of bases. 
Included among those are such issues as:

• Whether
  they criminalize activity that is protected by the Constitution.  A famous example of
  this would be the law that criminalized the burning of the American flag.  This law was
  successfully challenged on the basis that it criminalized activity that was protected by
  the First Amendment.


• Whether they are vague or overly
  broad.  There is a doctrine known as the "void for vagueness" doctrine which holds that
  a law must be specific enough so that the average person would be able to understand
  what conduct would constitute a violation of the law and what conduct would not.  Laws
  that are excessively vague are held to violate the Due Process Clauses of the 5th and
  14th Amendments.