I'm very happy with my faucet. It is a Delta Pilar and uses touch technology to turn it on and off. And can differentiate between a touch and a grap (to turn it). I also like that the lever is separate from the faucet (also operates on touch), as we have a ledge overhange behind (and above) the faucet - sometimes a unit w the handle on the faucet gets a bit tight against the wall/under a ledge, depending on the sink. To answer your specific questions:

1) Pull down faucet that is easily and neatly redocked.
Yes, very good redocking.

2) Have the ability to "twist" the head to be able to spray into corners of the sink without having to actually pull out the head. (I believe the Vinatta does this as someone posted a picture showing that)
Nope.

3) Have the ability to stay in "spray" mode without having to hold down the button. For example if you were washing lettuce you could have the faucet docked, water coming out in spray mode and still have both hands available to pull apart the lettuce leaves.
Yes!

4) Have the ability to have "spray" be the default mode when you actually turn on the water. (This is kind of like #2 in that the spray would stay on when the water running, but would also remember that you were in spray mode when you turned the water off and when you turn the water on again it's still in spray mode)
Yes!

5) Has a water-saver feature that allows you to temporarily turn off the flow of water at the faucet head rather than go back to the main on/off temp control.
Well, kinda in that one can tap it on or off. It will turn back on with a tap, at the same temp as before. The temp as well as turning the faucet on or off (or more or less flow) can be, of course, adjusted at the level.

Here is a link that might be useful: Delta Pilar Pull Down

surveymom - I am ROFLMAO right now. My husband is exactly the same way! I can spend forever researching a faucet only to have him shoot it down becuase it doesn't meet his expectations. Sometimes I think the faucet we select will actually have to cook for us before he'll be happy- lol! I keep dragging him to stores to look at them hoping that I'll wear him down soon! Please let me know what you select, I know he is looking for some of those same features.

Vinnata (I'm the one who posted the picture, btw):

1. Pull down faucet that is easily and neatly redocked.
   This is something that is subjective...I think my Vinnata easily pops back in...but it can be at any angle (see #2!)

Have the ability to "twist" the head to be able to spray into corners of the sink without having to actually pull out the head. (I believe the Vinatta does this as someone posted a picture showing that)
Yes...you saw the pic!
Have the ability to stay in "spray" mode without having to hold down the button. For example if you were washing lettuce you could have the faucet docked, water coming out in spray mode and still have both hands available to pull apart the lettuce leaves.
Yes, most do this nowadays.
Have the ability to have "spray" be the default mode when you actually turn on the water. (This is kind of like #2 in that the spray would stay on when the water running, but would also remember that you were in spray mode when you turned the water off and when you turn the water on again it's still in spray mode)
Ditto
Has a water-saver feature that allows you to temporarily turn off the flow of water at the faucet head rather than go back to the main on/off temp control.
No. But, like most one-handled faucets, you can turn it off at the handle w/o affecting the temperature setting (i.e., it "remembers" the temp setting by the position of the handle)

Now, if you get a Tapmaster to pair with your faucet...you'll have hands-free on/off control! You never have to use the handle or faucet head again to turn it on/off and the temperature "memory" is still there.

Here is a link that might be useful: Tapmaster

Thanks for all the advice! DH is happier. (when I told him he could actually get all 5 requirements by including a Tapmaster, he added a 6th feature - now make it affordable!)

chloe_s_mom - I was looking at the Pilar. Does it use some kind of battery to power the touch sensor? Do you know how that works?

buehl - yes, I thought it was you with that picture, but I didn't want to say, just in case I was wrong. Thanks so much. I do believe the Vinnata is in 1st place at this point. Now it is price hunting (and trying to convince DH that he probably can't engineer his own tapmaster for less money.)

nkkp - gotta love those men, don't you? 27 years ago when we were planning our wedding, we briefly called the whole thing off because of a dispute over the processional music! That's when I vividly learned about our very different styles of decision making. I like to think I've learned to adjust and bring him into the discussion earlier than I used to but I'm always on the lookout for minefields. Forgot about the faucet this time. Who knew that would be the kitchen "processional music".

The Delta Pilar does require a battery

I have the Moen Medora and I think it fulfills all your dh's requirements. Easy docking, head can twist while docked, can spray, spray feature can lock and there is a function where you can stop the water say to reach from the sink over to fill the coffee maker.

I have it in black and lucked out finding it as it's the only pull down that comes in flat black. I bought mine from faucetdirect if that helps.

Yes, as previously said, the Pilar does use a battery. And is relatively accessable (in order to change). Works with using the level too (in case the batteries run out)

We have a Price Pfister that has all but #4 on your list.