I have worked on projects as large as 100 million square feet and on those projects we only sometimes used permit expediters. It depended on the complexity of the project, the site location and the city, state or country we were working in. Now that I am working on mostly restaurants and bars there is no need for permit expediters in my world, but there still may be in yours, so I will take this time to explain what they are and what they can do for you.
First, I would like to point out that if you are working with a design professional that understands the permitting process you should ask them if they think you need a permit expediter. They may be able to get you through the permit process without any problems which would make hiring a permit expediter unnecessary.
The lowest level of service a permit expediter provides is to take the plans from the design professionals and drop them off at the Building Department for review. Be careful that you understand this takes very little effort and shouldn't cost you much at all. I've seen expediters charge up to $5000 for this service, knowing their clients thought they were contributing more to the process. These expediters only provide the service of submitting the plans to the City. You, your designer or architect or your contractor can do this as well. These expediters usually don’t fill out the forms, they do not necessarily understand local codes or zoning, they will not negotiate with the officials for you, nor will they pay plan check fees on your behalf. Consider them a courier service and no more.
A full service expediter does more but you should not expect them to understand local codes or zoning. They count on the design professionals to do that. What they will do is tell you how many plan sets you need to turn in and whether they need to be wetstamped, they will organize landlord and owner's authorizations in buildings where it is required, they will fill out the forms and they will tell you how long you will have to wait to receive your permit. For most permits your design professional can do all of this without the help of an expeditor unless they are inexperienced.
Permit expediters can also provide services that can help you obtain liquor licenses, beer and wine permits, conditional use permits, 24 hour permits for single events, zoning permits, feasibility analysis, site surveys and some due diligence services. It is in this area that I find expediters most valuable. Again, make sure that there isn't someone already on your team that can help you with these items. Your design professional will advise you well.
Most of the time an expediter is hired because of their relationship with the people at the Building, Planning or Health Departments. If your project is complicated or unique in a way that a good relationship will help to speed up the process, you may want to consider hiring a permit expediter.