This is how I got it to work (miraculously).
First, using the web-based flash settings, add the "www.midomi.com" URL to:
- Global Security Settings
- Website Privacy Settings
You can see what I mean by seeing this guys instructions here.
Once you're done doing this, open the midomi website in a new window. It is very important that you do this, otherwise the settings may not apply.
Now here is the part where it gets weirdly interesting.
On the midomi website, just record anything for about 5-10 seconds. It will then take you to a link where it will say "Nothing found". On this page, look for a link called "Test your microphone" (URL might look like this)
After clicking on this link, it will take you to a sort of test area. Here you can specify which mic you would like to use. After choosing the appropriate mic, you should be able to record something.
This might help anyone trying to connect an external device as a mic (midomi seems to always choose your internal device by default).