TURTLEONMAC  It seems that as of 10.5, you can't poke around in the memory of other applications without proper authorization (I was always surprised you used to be allowed to).

Anyway, it seems you can get this version of the cheat to work by making it execute as root. To do this, open up terminal and navigate inside the application using something like

cd /Applications/Games/The\ Cheat.app/Contents/MacOS/

You'll need to use a different path if you've placed the application in a different place than I did. Then type

sudo chown root The\ Cheat

followed by your admin password, then type

sudo chmod +s The\ Cheat

This should make it work again. Note that you'll have to repeat the steps if you move the application.  
(Version 1.2.1)

GAME_ON  Thanks, man. I guess it would make sense for it to need root privileges to scan other processes memory, huh?

I think that'd be something to put in the next update to The Cheat.  
(Version 1.2.1)

CRASHDUMP  Here is a new version who works with 10.5 Leopard: http://www.crashdump.fr/apple/the-cheat-122-pour-leopard-540/  
(Version 1.2.1)