By Distributing Computing I am taking the definition to mean a system that requires more than one physically distinct sub-systems to operate (that is, more than one computers).
First check, can this distribution be simulated on one computer with all of the components installed? If so, this provides reduced cost for certain types of testing that don't need to full distributed environment.
Configuration testing becomes increasingly important in distributed systems. Unless you can be guaranteed homonogenous sub-systems, you will need to be aware of the system works with several different sub-systems -- possibly configured by a variety of different people in absense of a uniform management plan.
Fault tolerance testing becomes more important in a distributed environment. As you increase the distance between machines, and increase the number of machines and transition points, the number of points of failure increases. On a single machine you can often assume a guarantee of service for that machine, in a distributed environment you need to decide which guarantees of service you assume, and which failures need to be mitigated.
Those are just a few of the things that came to me right now.