Disclaimer: The following is my take and is not meant to be a definitive analysis of the petition.

Para 1:

Use judicial means before attempting brute force.

Para 2:

Don't equate national governments with terrorists groups existing within national boundaries. Don't blame the govenments without producing convincing evidence of active cooperation.

Para 3:

Don't equate civilians with governments; don't blame or punish civilians for the actions of the governments

Para 4:

No Nukes. No Biological weapons. No Chemical weapons.