Logger: Consider logging locally-generated messages along with received ones

[solardiz]

Right now, the logger uses syslog(3) to log its own events, such as new or failing client connections. Maybe (or maybe not!) some of those should also be recorded along with received messages from the same client, yet somehow be clearly distinguished from them.

For example, what if a malformed message arrives from a client - should we communicate that event further, via our log reporting tool, or should it remain buried in system logs that are not read by the tool and are retained for a different period of time (probably not ideal)?