If your 2G's headphone plug's microphone input is broken, I'm not sure what options you really have. It seems like Apple is dead-set on that being the ONLY audio input method for older iPod touches, for whatever reason.
It's possible that the Blue Mikey 2.0 will work (everything on their website indicates it should), but just to give you a little history, when iOS 2.2 came out, people discovered that some of the 30-pin dock connector microphones made for the iPod classic and Nano all of a sudden worked on iPod touch, even the first-gen! This continued to be the case once iOS 3.0 was released, but then when 3.1 came out, Apple artificially disabled use of several of these mics (a very popular one was the MacAlly iVoice III; there is also an iVoice Pro that has a built-in speaker, and there still seems to be some debate about whether the Apple-enforced software block only affects the III or if it also affects the Pro as well). I have an iVoice III, and can confirm that when you first plug it into an iPod touch 1/2/3rd gen, or an iPhone/3G/3GS, it works for about 15-30 seconds, and then the OS blocks it and pops up a dialog telling me it is "incompatible" (even though it was working just a moment ago!).
The software block for the iVoice is still in place today, through the entire 4.x series as well as 5.0. And it doesn't look like anybody in the jailbreaking scene/community has bothered trying to work around the restriction.
It's possible that Apple specifically targeted only certain dock-connector mics with the software block they introduced in 3.1, and that Blue has an arrangement with Apple (paid the appropriate licensing fees, etc.) whereby Apple continues to allow their mic to work. I don't have one of those 'phones, so I can't test it. And $80 seems a pretty steep price to pay for a mic to me...if you decide to go this route, I hope you can find one for less (even second-hand), otherwise you might as well sell your 2G touch and then use that money towards the purchase of a 4G.
It sure would be nice if you could pair a bluetooth headset to an iPod touch, but again Apple has blocked this. You can pair stereo A2DP headphones, but if your stereo bluetooth headphones include a microphone, the iPod won't see it (unlike the iPhone), and if you try to use a normal telephone bluetooth headset, the iPod won't see it in a scan when you try to pair it. These are both because the HFP (hands-free profile) and HSP (headset profile) Bluetooth profiles are not included with the Bluetooth software stack that comes with the iOS version made for iPod touch. Apple lifted this restriction with the iPod touch 4G, so that you can use a Bluetooth headset for Facetime, but all versions of iOS for the older touch models through 4.2.1 (for the 2G) and 5.0 (for the 3G) block HFP and HSP bluetooth devices from pairing. Again, it's a stupid artificially-imposed Apple software limitation. The original iPhone couldn't "officially" use A2DP Bluetooth devices when 3.0 was released, and someone managed to find where in the software Apple was enforcing this block (it was in the /usr/sbin/BTServer daemon) and wrote a patch to get around it. I imagine that the HFP/HSP block is being enforced in much the same way, but nobody with the skills to work around it seems especially interesting on working that problem.
-- Nathan