I use syslog message routing mechanism to log high-priority messages
from my python code to separate file.  When exceptions are logged, only
first line routed to specified file, and the rest goes in /var/log/messages.

Such problem exists when SyslogHandler instantiated with "/dev/log".

If logging is performed to remote host via udp socket, then exception
logged as one long string with all lines being concatenated.

Probably multiline log messages should be automatically splitted and
logged line-by-line with the same facility, severity and program name.
Also it will be good to have special formatter tag which expands as
empty string in first logged line, and as user-defined string in
remaining ones. This can simplify automated log analysis.