You can clay the bug residue.
After, you can use many cleaner type waxes or paint cleaners. For example, I have used Moose, Wax Vanilla Moose, AIO and PwC.
Also, you can buy dedicated plastic cleaners at places like Pep Boys. You can get Meguiar's or Mothers. There is also a plastic cleaner from Blue Magic (I believe that's the name).
If the headlights are yellowed, you can use Flitz or some here have used metal polish. If you look under Lynn's posts, she has a nice write up on the process of rejeuvenating dull plastic lights.