Strange, I cannot replicate the problem of the missing third button.
I never used the Mighty Mouse on my two iMacs (office and home), I plugged two cheap mice (a 5 buttons one at office, a classic scroll mouse at home) with no drivers.
Never plugged a mighty mouse, and I can configure all buttons from the Expose/Spaces preference panel, that detects the extra buttons.

The only two functionalities you miss (as they are present in the Mighty Mouse pref pane only) are "Application switcher", "Spotlight" and "Other..."

Mi problem wasn't that the button didn't show up, it was that I didn't get the extra options as in the Mighty Mouse settings. Most notably the Application Switcher, which was the one I wanted.

@tuckerch:

Yes I also found several app's, preference panes, drivers, etc... But why pay when you can hack for free (apart from the fact that I have no means (credit card) to pay for software over the web ;-( ).

@llee.

As I said in the hint, I changed ALL instances. And don't forget to unplug, load the new .kext, and then replug you mouse.

@tempel:

Since the preferences "stick", you can put the .kext back to its original form and your changes will survive (at least several on my 10.4 installation) updates.