Seems to be a combination of problems. Bites from cage mates certainly can get infected easily, especially given nearly 14 are in each cage and babies do poop alot. I would separate into groups of 4-5 in roomy cages and isolate those who are showing any sign of injury to legs or tail.
The fact some appear to have webbed feet or improperly grown toes, could mean defects in the hatchlings themselves, either from fluctuating incubation temps (if it got too hot for a short period of time, birth defects can occur) or genetic defects. As all North American bearded dragons are genetically related to some extent or another, it is possible to have recessive negative mutations come up, if both parents carry the recessive mutation. If this is the first clutch that showed any such problems, (and I do beleive you mentioned you have bred them before, though not sure if the first clutches had simplar problems) it could be a problem with the incubator you use. However if you have more than one clutch in the incubator and they all hatch up fine, then it could be a genetic problem that doesn't come up all the time. May be a good ideal to switch the male with this female next year to see how that goes.
You can always call your vet and ask him how much it would cost to get X amount of bearded dragon babies euthanized. He may give you a good price. The only other method I can think of that is humane and should work with bearded dragons is building a CO2 tank. Many people (especially snake owners) who breed their own feeder mice/rats use these tanks to humanely put down their feeder rodents. It takes a bit of money to set up, but typically fairly cheap to maintain. You basically use a tightly sealed jar or small sealed box (made of acrylic or glass sealed tightly with a tightly fitting lid) with two hoses coming out of it. One on top and one near the bottom. The top hose usually goes into water, so air can be pushed out of it, but not be sucked back in. The lower hose is attached to a CO2 tank (like the propellent tank for paintball guns). SOme people also use dried ice to produce CO2 but I don't know for sure how that is setup (if the ice is put directly into the kill jar or in a separate jar). THe biggest cost is the refill hose used for the canister of CO2 and the canister itself. I have included a link on how to make this kill tank below, as I was just goign by memory above and may not have all the details right.
If you have friends who own snakes and breed their own feeders, ask if they have a kill tank you can borrow, to put your bearded dragon hatchlings to sleep. They may be happy to let you borrow it, or offer to put them down for you. Maybe offer some money to cover the cost of CO2 used, which shouldn't be very much. ($5-$10 is probably all it costs to refill the CO2 canister)
www.junglemistreptiles.com/co2.html
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PHLdyPayne
LOL.
