I cut my hunting teeth on those guys, shooting them from the age of 7, eventually with everything in the gun cabinet, including, but not limited to muzzleloaders. They were considered a pest on the ranch where I grew up, and it was said 7 jackrabbits could eat as much as 1 cow.
They are excellent eating if you get a young one, about 1/2-3/4 grown. Older ones can get pretty tough, but can still be cooked until tender enough to eat. The taste reminds me of venison more than cottontail, I guess it is because of their diet, which is closer to that of deer.
As far as nasty diseases, their no different than cottontail or squirrel. Fleas and ticks are the main vectors, although they can also have internal parasites. Wear gloves when handling them if you are worried about the fleas and cook them thoroughly. I've left plenty of old ones on the ground for the buzzards, but would not leave a young one. Try it sometime.