Ah, great video, although I believe it has been posted here before. Anyway, can remember someone's comments on the "A Flat Minor/Miner" joke

I think it's kinda cool of him to joke around a little
I watched the video again, but think I missed the parallel 5ths comment. At what time is it mentioned? Anyway, when two voices (or separate melody lines) that are a perfect fifth interval apart, both move in the same direction and end up forming another perfect fifth interval, it's called a parallel (or consecutive) fifth. Most likely they both move up the same interval, but they could be inverted or an octave+fifth apart, that really doesn't matter.
The "ban" on using consecutive fifths in classical compositions started in and around the renaissance I think. Argument was that the melting into eachother of the overtones (that's what makes "powerchords" sound so good with a little distortion on!) took away the individualty of the seperate voices. Check out
this if you want to read some more.
Avoiding parallel fifths seems to be something specific to typical multi-voiced renaissance music, so a comment like that is most likely to come from someone with a classical education. Mind that that type of music (called polyphonal) wasn't exactly chord-driven then (I can imagine them being puzzled by
PlaneTalk for example, if it's anything like I think it is).
Most contemporary music, however is chord-driven with a single dominant melodic voice (homophony). It SWARMS with parallel 5ths. Hell, if you really wanted to upset a renaissance composer: take your mp3 player, travel back in time, and let him listen to any rock/punk song with only powerchords
