This information is logged on the Sling servers. If this is a security issue, e.g. you suspect unauthorized access to your Slingbox, Sling support may release some info, if you can convince them that you are the rightful owner. It may be easier for you to just set new admin and guest passwords and see whether the trouble stops.
There are logs written by the various players, but I don't think that's what you are looking for.
AFAIK, there are no user-accessible logs kept on the Slingbox itself.
There are various ways you could get a computer to "see" the Slingbox traffic. You could then capture it with Wireshark and analyze to your heart's content.
What kind of information are you seeking?
The Slingbox might have a "syslog" or similar capability, but I know nothing about that; perhaps another member can help.
Otherwise, you will have to get your PC to "see" the Slingbox traffic. See http://wiki.wireshark.org/CaptureSetup/Ethernet
Once you get that working, you can capture Slingbox traffic. This could be quite large if you have fast upload or it's viewed for hours on end, so you may want to set a filter to capture only packets to the Slingbox (which is far less data than the returned video).
Then, use the Statistics->Endpoints->IPV4, which will give you a nice chart showing packet count from each source IP address. Lookup those addresses, e.g. at domaintools, to see ISP and approximate location.