FAT16 disk refuses to mount in Mountain Lion
I eventually got the disk to mount whilst retaining compatibility with my bootloader. For anyone wondering, the compatibility conflict was in the FAT BPB (BIOS parameter block). Basically, the BPB has a field for specifying how many sectors compose a FAT cluster, where I manually supplied a value of 1. However, changing this to 4 fixed the issue. For more information on the BPB, you can see this reference page (you want to look at byte 13).

For anyone stumbling upon this answer randomly, this basically means that some older disks (such as floppy disks copied by dd) may not be able to be mounted by OS X Mountain Lion any longer. This is just a hypothesis based on observations of my own project, but hopefully this helps someone else running into this far-fetched issue.