I first watched Firefly (starting with the pilot) while waiting for netflix to send me my disks of Angel Season 5. So I was already in a Whedon-frame-of-mind.
I remember thinking that the first half dragged on quite a bit, but was completely hooked when Kaylee was shot. Jayne's moment of quiet contemplation while looking through the sickbay window was gut-wrenchingly sweet and so telling. This was after he rudely embarrassed her at the supper table. It's just how families are - crude and fighting and getting on each other's nerves, but when it really matters, the love shines through. (god, that was sappy - sorry)
Oddly, the moment I fell in love with Mal has not been mentioned here before, I think. It was when he shot Patience's horse. Now, I love all animals, don't get me wrong, but it was such a unexpected move and seemingly the right thing to do in such a situation. Still - nobody purposely shoots the horse! Brilliant.
That's all I can think of for now.