Patrol missions are mainly used to collect upgrade items, complete bounties, complete small missions to increase vanguard rank, participate in public events and item farm. Earth hosts one of the best loot farming locations (look at the Item Farming section of the FAQs portion of the guide for more details).
The upgrade item that can be found on Earth is spinmetal (examine the upgrade item section of the FAQs portion of the guide for more details).
Mission rewards: +25 Vanguard reputation for target missions. +10 Vanguard reputation for all other missions.
Due to the simplicity and general lack of difficulty involved with them, missions are broken down to types.
The mission types that are available on Earth are:
Target mission: Head to the marked location and kill the target enemy (examine the objective for target information)
Scouting mission: Head to the marked location and either stand at the designated spot, or scan the piece of equipment indicated
Collection mission: Examine your objective for the item required and from which enemies it drops. Then find them and take 'em down.
Culling mission: Kill a certain number of enemies and the mission will be complete.