OK, I got the PowerMate Bluetooth to work with an older (not-BT4) Mac and the IOGear GBU521 USB Bluetooth adapter. This adapter uses the BCM20702 chipset from Broadcom, which appears to be natively supported by recent versions of OS X, so I assume any adapter with the same chipset should also work fine.
Here's what I had to do to get it to work on an older Mac and the USB Bluetooth adapter:
1) Make sure you are using the newest version of the PowerMate software, currently confusingly called v1.0.1 (yes, that's right, it's newer than v3.1).
2) If the Mac appears to be favoring its internal Bluetooth over the external adapter, use Apple's Bluetooth Explorer to change it. You will need a Developer account (free will do) to obtain this from the "Hardware IO Tools for Xcode" download from developer.apple.com. Older versions of Xcode actually came with this, but Go to Tools | HCI Controller Selector, and choose the IOGear device (listed as Broadcom Corp since that's the manufacturer). Click "Activate." It says this won't persist after a reboot, but I have found that it actually does. (In related news, some people claim the Mac uses the USB Bluetooth without any need for this at all, while others said a reboot alone worked. I, however, did not have such luck.)
3) Pair the PowerMate Bluetooth to the computer with Belkin's software. If it is not showing up, you may have to go to "Low Energy Devices" in Bluetooth Explorer and manually connect it, then use the software--I can't imagine that this is necessary, but I did it before I realized that I needed v1 of the new software (confusingly, same name as the old one which was at v3.1) to make it work.
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As for the PowerMate software itself, I am very disappointed in the new version. One notable feature missing is that you can't use more than one USB PowerMate at the same time with the new software--and not only that, but you can't have more than one connected at the same time. I think one USB and one (or possibly more?) Bluetooth PowerMates would work, but I don't see why they have this limitation.
Second, in case you want to try to work around this problem, you can't. You can't run both the old and new version of the software at the same time, even if you want one to control USB and the other to control Bluetooth.
That being said, I do think the new software as a slightly better UI than the old one in that it's easier to create actions for PowerMate events. They're all listed and you can choose what you want. I think it was more cumbersome in v3.1. The only thing worse is if you want to run an AppleScript in response to a PowerMate event; previously, you could just type it in, but now you have to choose a file.
I hope they add back the missing features--notably the ability to use more than one--or just at Bluetooth support to the old software.