When minecraft.net is not available for login validation and Play Offline is chosen, connecting to a multiplayer server that is also set to offline mode yields:
Connection Lost
Internal Exception: java.net.SocketException: Connection Reset

The message in the server log is:
java.io.IOException: Received string length longer than maximum allowed (25 > 16)
at ef.a(SourceFile:235)
at cy.a(SourceFile:30)
at ef.a(SourceFile:192)
at cg.i(SourceFile:249)
at cg.c(SourceFile:15)
at ch.run(SourceFile:93)
(date:time) [INFO] /(player ip) lost connection