Checkmate???

this would technically be putting black into checkmate in a blitz game, and yet any arbiter would obviously allow black the next move to take white's king winning the game.

To be really legalistically technical about (and that is the point of this discussion I think) the arbiter does not allow black to extend the game beyond white's checkmate in order to "take the white king" -- taking the king is just a commonly accepted way of showing-proving the real game winning condition, which is that white has made an illegal move. Black wins because white has made an illegal move in a blitz game. Black's taking the white king would _not_ be a part of the game score, the game ends 0-1 when black claims victory citing white's illegal move.  But there is, in this, a slight retroactivity, because the claim comes after white's move... but the condition the claim is based on is simultaneous with white's move. 

If the game was being played with regular time controls... I think the conditions of touch move are enforced, but there's no other penalty and in fact if white has no legal moves with the piece he touched, he's free to make correct his illegal move by making any legal move he wishes (I don't know how the arbiter rectifies the clocks). 

Thats kind of what I thought it might be.

Also, to clarify... in tournament conditions at regular time controls... what exactly happens when i put my opponent in check and he makes an illegal move? I claim an illegal move and he is held to the touch rule if he has a legal move with that piece?

I would imagine the proper way to handle this situation is to stop the clock, bring over the arbiter or TD for the discussion?

Which brings up another question... when a dispute happens, is it customary to try to clear things up between the players first, before a third party is involved? Or is it always necessary to call over a TD before the discussion begins?