Ah.
The biggest web-desk difference in implementations for me is the network access - in a web solution there's no harm in pinging another server with a bit of data; with a desktop solution - I don't want to bother the network all the time (Resharper's error reporting springs to mind).
That means that "issue merges" should be done client side; which means I need to store "previous errors" and send a batch periodically (or on command); which means a naive log4Net appender isn't the right tool for the job.
Unless this custom appender will start a thread to poll a directory for new outgoing messages... (and that doesn't sound right)