hitting the clock late

In some games of mine -- usually blitz -- my opponent doesn't hit their clock after moving (and releasing the piece).  I know I can just let it run, and sometimes I do for a while, but sometimes I go ahead and move.  Do I still need to hit my clock after moving?  Anyway, supposing I do, but in reaching for the clock, my hand hits the clock before my opponent's does (he is hitting late for his previous move) and takes some time off my clock (perhaps a second at most, usually).  If I lose by a second, do I have any valid claims?   

If you've already started moving your piece, I can't see why the other player would hit the clock... I usually just tell them they forgot.

You won't lose more than a millisecond... and until you hit the clock they have every right to hit it.  ... if they're deliberately stopping you from starting their time.. that's different.

Well, it usually works out fine, and I'm sure it's almost always unintentional on their part.  But every once in a while, I'll lose by that split-second, then I end up regretting not making a claim.  

Still, my first question stands:  given that I don't even have to move, but supposing I do move, do I then need to hit my clock after moving if they didn't hit on their previous move?  It's their clock that's running the whole time anyway, and hitting my clock merely keeps theirs running ...

If they forget to hit the clock, and you move your piece, you dont have to click the clock (since their time is ticking). If you move your piece, let go, and then they hit the clock realizing that they forgot to this isnt allowed (anyway why would someone do that).

I either don't move and let their clock run, or I tell them. Usually I wait a little bit though.