I tried updating to slimserver 6.2.2 (From 6.2.1) using your standard Mac installer. slimserver 6.2.1 was NOT running at the time. However, the 6.2.2 installer reported that slimserver is running and I must terminate it in order to do the update.

Here's the likely cause: my Mac's hostname is "slimserver". As soon as I changed the hostname (to "slim"), the update worked flawlessly.

I'll bet the installer does a "ps" and greps for "slimserver" to see if the server is running. If so, your regular expression is too permissive.  My Mac was running OSXvnc (http://www.redstonesoftware.com/vnc.html) which includes the hostname in its ps entries, like this:

/bin/sh /Library/StartupItems/OSXvnc/OSXvnc-keepalive /Library/StartupItems/OSXvnc/OSXvnc-server -rfbport 15900 -desktop slimserver -alwaysshared -restartonuserswitch N -keyboardloading n -pressmodsforkeys n -swapbuttons -rendezvous y -rfbauth /Library/StartupItems/OSXvnc/.osxvncauth