There is NO single pattern. There are Singleton and SingleCall.
With SingleCall, every client gets a new object, so you don't have to
worry, until you do not access any shared resources.
With Singleton, all clients share one and the same object, so the thread
safety can become an issue, and you have to take care.

Not remoting related, but Jon Skeet has excellent article about threads
and thread safety, so I highly recommend to read it:
http://www.yoda.arachsys.com/csharp/threads/

Cheers
Sunny