what determines who leads the flock as they take off from the lake, river, etc. Are there various leaders or is it the same one.
I believe the geese (or any bird which flies in formation) alternate. Ususally, I think, the older or stronger birds will lead the flock, allowing the weaker or younger ones to fly in the middle or the back, benefiting with an easier flight due to the wind effect of the leaders (I don’t really know how to explain this - kinda like racecars following closely to save gas??). During the flight, the leaders alternate, so that no one bird does much more work than any other (though I imagine the small and weak must pretty much just stick to the back and hope they don’t fall behind).
I haven’t looked this up, though, so I don’t really know details…this is just the little input I was able to dredge up from the depths of my memory…
While watching an unusually large pack of geese fly last weekend, it struck me that I’ve only seen geese fly South in autumn, but never back North in the spring. I assume that they fly back, instead of walking, taking the bus, or shipping goose eggs to the North by Fed-Ex. Do they not fly in formation on the return trip?
They do fly back north, but only when you are not looking. 
Yes, they do fly in formation on the return trip, but not necessarily always in the same flock. Sometimes flocks will split apart into smaller flocks, or two flocks will join together into a larger flock. Flocks will arrive in their northern breeding grounds at different times - some will arrive early in the breeding season, others later.
Of course not all of them will not complete the trip back north, just as not all will complete the trip south. There are factors like disease, hunting, poison and predation to contend with, not to mention the fact that, Canada geese in particular, will often settle in an area with plentiful food, marry one of the locals and start breeding hybrids.
Of course, some birds do fly ‘NORTH’ for the winter.
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(Chimney Swifts and Swallow-tailed Kites fly from South America into the US during the Southern Hemisphere winter, staying from about March to October for breeding, then flying back to South America en masse.
Since we’re on the subject, I thought I’d bring up a question I recently got.
Someone stated that when migrating geese fly in a vee, the right arm of the vee is consistently longer (has more geese) than the left (leaving out the center goose).
This seems highly unlikely to me, but not having actually counted flocks, I can’t refute it. And as I don’t live in a place with migrating geese, I can’t go out and count any.
If anyone actually has an opportunity to count a few flocks, I would appreciate it if you would you e-mail me the counts (via my profile).
BTW, I can confirm that mnemosyne has the basic thinking on the subject correct, although I believe there may still be a some controversy on the subject. The following geese benefit from the wing turbulence of the preceding one (though I can’t explain the exact aerodynamic advantage offhand). Some researchers contend that the leader also gains an advantage, although not as much as the followers, although again I’m not certain how this is supposed to work.
I recently saw something on a flock of young Sandhill Cranes that were being trained to migrate by following an ultralight, that would “surf” on the turbulence off the wingtips and form a vee with the plane as the flock leader.