I am running Python on a Raspberry Pi and everything works great.
I have a small script running on the system start up which prints several warning messages (which I actually cannot read since it is running in the background)...
My question is: Is there a way via SSH to "open" this running script instance and see what is going on or a log file is the only way to work with that?
Thanks!
Try using the Python logging library.  You can configure it to save the output to a file and then you can use tail -f mylogfile.log to watch as content is put in.
EDIT:
An alternative is to use screen.  It allows you to run a command in a virtual console, detach from that console, and then disconnect from the machine.  You can then reconnect to the machine and re-attach to that console and see all the output the process made.  I'm not sure about using it on a script that starts when the machine is turned on, though (I simply haven't tried it).
Python on system start up