Time Machine only backs up /Users and /opt I have 2 MacMinis.  The two MacMinis are both connected via firewire.  I have one MacMini backup over afp over firewire to a hard drive on the other MacMini.  This system works perfectly and the whole MacMini gets backed up.

I have a MacBook.  The MacBook has the same system, but does not have the firewire connection and only backs up over WiFi.  When I look at the backup of the MacBook, it only has the Users folder and the opt folder.  No errors are reported in TimeMachine, and no files are in the Exclude list.
Select Options… in System Preferences » Time Machine and specify which directories you don't want backed up.

theis answer shows, what happened on your device:

Time Machine Synchronize just my Home Folder to external hard drive in MacOS Leopard

So you have to do it the other way round