It appears that if you're not using the JRun version of Flash Remoting, passing RecordSets to a Flash client fails unless the ResultSet is still connected to the Database. As leaving ResultSets connected to a database is a truly bad practice, passing Java RecordSets via FR (without JRun) isn't practical.
Our Slideshow Demo's Java code shows one possible workaround using CachedRowSet instead. This returns non-fatal errors but seems to work otherwise.
Another workaround is to translate your RecordSet into Arrays, pass the Arrays, then translate them back into Flash RecordSets once they arrive at the client.
Rumor has it that Macromedia will be releasing a patch that supports RowSets and fails more gracefully for ResultSets sometime soon.
If you have information on other possible workarounds, please send us a post.