Nice Youtube find, Oldhat. That video pretty much sums up everything I know. Changing one note of a dim7 = Dominant 7 was news to me.
Mreisz, I also like your idea of a 1 in 3 chance of hitting the right dim7, funny. If you do hit the wrong dim7 chord you could slide it up or down a fret and your odds would be 50/50!
As far as the "usage" knowledge I have to chip in, the dim7 creates tension like the Dominant 7. That's why you can substitute like they explain in the video.
In the Key of G major, the D7 wants to resolve back to G (V7 to I.)
The F# dim7 REALLY wants to go back to G (vii dim7 to 1.)
If you look at the chord top down( as per the D7-ish shape with the D# on the fourth string on the guitar):
F# wants to go to G
C wants to go to B
A wants to go to G (or B it's caught in between)
D# wants to go to D
Since Em is the the relative minor of G, it also can create tension to go to Em. That D# can want to go to E as well. So if you're playing G and an Em is coming up, your could whip out the F#dim7 and to walk it down to Em, or play a lick with those chord tones and create tension to set up that Em.
You can also use that dim7 to set up a Key change ( like G#dim7 to A)