I bumped into this issue a while back. While I'm not sure this is the "best" way, I too ended up relying on cmd() failure to figure out whether I was truly logged in or not. In my case the remote machines were all unix/linux based, so I'd issue a simple "uname -n" and see if I got back the same hostname as I was expecting. If the call to cmd() failed, I'd propagate the failure. If the call to cmd() succeeded but the hostname didn't match...well that was a whole other sort of error (which in my case never happens in practice...but it can't hurt to check).
One thing I noticed with the various calls to Net::SSH::Perl is that there were two ways to fail...ungracefully, which would die/croak...and gracefully, which would return actual error codes and messages. So consider encapsulating the various calls to "things that might fail" within eval blocks. Then you can check $@ along with the various arguments that are returned via the calls to login(), cmd(), etc.
P.S. I don't happen to have the code in front of me at the moment, but /msg me if you want to check out my 'cascading' failure with Net::SSH::Perl that pretty much guarantees a working connection or a meaningful error. I'll repost it on request (but don't feel like re-writing it on the fly).