I know you can edit records (including Work orders) in Salesforce1 but when i am trialling Field Service I cannot edit a Work order.
My user is now set to the System Administrator profile so I can't believe their are missing permissions.
The documentation states with the app you:
The mobile solution provides access to critical information regardless of connectivity, and uses automated processes to support a full range of fi eld activities, from sending and receiving real-time job updates to managing work orders and speeding up manual administrative work. It even enables users to generate reports, access knowledge articles, update parts required, and capture a customer’s signature.
It states "managing work orders" as a feature but I can only see features for creating a service report, a new task, opening in salesforce1, adding to the feed and getting directions.