Queuing web service calls
If any locking on _queueItemLock is happening inside a lock on _queueLock then you can consider this as thread safe.  

If any access of _entryCount is done in a lock on _queueLock then you don't need the Interlocked.Increment(ref _entryCount); but you can just increment in the normal way.  

If you by any chance are using C# 6.0 (VS 2015) you can use string interpolation by using the $ operator without the need of calling string.Format() like so  

Logger.Trace($"Running task queue item for {_methodName}.");  


other than that there isn't much to say.