Discovering these roadblocks is like the optimization of a program. Observation is the key for Agile Coach. Being in listening mode is tough to do :-) but understanding what teams are doing? How team members interact with each other? usually is done for several days or few weeks at-least. This helps in unveiling issues that hamper teams progress, waste or re-work.
From my experience I have observed, there are times when teams are working on agile but they really don't understand what agile is, or they are not comfortable about right approach of process or even worse they are not even sure what is the end goal of product or project they are working on, which eventually leads to either paralysis of team or individual.
Once primary issues have been identified, Agile Coach will then work with teams and management and facilitate improvement of issues. This obviously should not involve what they are doing wrong but its rather guiding them on the discovering better approach.
Like agile, agile coach should define the road-map and has to work on bringing improvement over time. We can not bounce change over people, it has to come with time. We are there to help, hence talk, collaborate and gain trust for people to not resent or push the change.
However a Coach works, and whatever approach they take they the Coach needs to avoid creating a learned dependency.Coaches need to be able to withdraw when the time is right and let the learning continue..
P.S - Start Simple, be a good listener....