Another legitimate use of partial classes is to help reduce the "monolithic web service" clutter in WCF. You want to to break it down into logical groups of functionality but don't want to have to create a ream of individual service instances/endpoints (presumably because they share state, resources, and so on).
The solution? Have the service implement multiple interfaces, and implement each interface in its own partial class. Then map different endpoints in the configuration to the same physical implementation. It makes the project a lot more maintainable, but you still only have one physical endpoint.
In some cases I'd point to this type of approach as a poor practice on account of the SRP, but when you're working with WCF services or web services in general, it's not quite so simple. You have to balance internal design requirements against external consumption requirements.