Not dumb... I've seen professional writers create larger plot holes than *that*! Look at the Harry Potter books; they're much fun to read and they're very popular - but let's face it; they all have plot holes large enough to ride broomsticks through!!!
Anyway, for all I knew the Youtube thing was a deliberate set up for a later development in the story.
If this is not the case you can easily edit the story details to eliminate this flaw if you think it's important enough to. Say that the girls found an incriminating DVD in the teacher's desk or out in the school parking lot or something - perhaps it was something the teacher made herself and misplaced/dropped. A bit dumb of the teacher perhaps but we ALL make mistakes.

Then they'd have a real blackmail hold on her (they can threaten that they'll put it on Youtube themselves) - until they make the mistake of not protecting themselves (that is at least a realistic mistake for a person - especially a teenager inexperienced in intrigue - to make) from capture.
Even as is, what are the chances that someone else who happens to know the teacher will stumble on the Youtube video and try the same thing? Not all that great, really; you know how many videos like that (sans nudity) are in there? A video as descrivbed probably wouldn't last long anything before it got flagged/deleted, leaving no blackmail evidence on the teacher. of course, then she'd still wonder who the devil put that thing on Youtube in the first place (if you wanted to go with *that* idea instead).
In any case, I hope you continue with the story; it definitely shows promise.
Dare to be different... and make a difference.
To boldly go where no one in their right mind has gone before...