The MIDA Multitool is the best weapon for patrol. I use it with Blackhammer (the pwner of fallen walkers) and Hunger of Crota. The insane stagger disables the enemies that can survive head shots. The accuracy on the MIDA is insane. I hover around 75% precision kills and have seen people with over 90%. The main ability makes you move faster and helps you get to objectives / material drops faster.
Rating 10/10 for patrol
Anyone else use it for patrol? MIDAless folks do not fret. Xur is rumored to sell it soon per megaman.
[spoiler] Awesome at the first part of Crota's End too. [/spoiler]
Edit 1: honorable mentions:
Fang of Ir yut
Bad Juju
Fatebringer
The Vex
Whatever gun you are testing / leveling
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I'm upgrading my red death and I've reached the second perk of the gun and it's one of most useful perks around. I don't need to take cover anymore, especially with a Titan; makes me feel like juggernaut.