I guess I'm a bit behind the technology curve. The MacBook that I'm using as one of my development machines is one of the original white Intel MacBooks with a Core Duo CPU (not Core 2 Duo). It's a 32-bit machine, and Apple doesn't offer Java 6 for 32-bit computers.
Mint, however, requires a version of Java 6, which is why we recommended using SoyLatte to run Mint. That comes with all kinds of inconveniences because SoyLatte uses X11 for its GUIs, which means DrJava needs to run under X11.
Yesterday I tested Mint and DrJava with Mint using Apple's Java SE 6.0 Release 1 Developer Preview 6 (file name: javase6release1dp6.dmg), which I still had floating around and which is the last version of Apple's Java 6 that still runs on 32-bit Macs. It works! SoyLatte is only required if you don't have a version of Java 6 (either Apple's official version on 64-bit Macs, or Apple's Java SE 6.0 Release 1 Developer Preview 6 on 32-bit Macs) on your Mac.
I have updated the instructions on how to install Java Mint on the Mac and how to run DrJava with Mint accordingly.