None at all. It's best to check with the breeder before hand if there's any history in the lineage and ask as many questions as you need to. Most definitely look to get a Border from a breeder, (with or without papers, depending on if you want to breed and/or show them.) They're hardy dogs, but you can never trust pet stores with purebreds.
As they reach their teens, Borders are prone to arthritis like most medium to large breed dogs. (My last dog was very stubborn about his arthritis and refused to slow down, even when he was fourteen.)
But overall I'd say the biggest problems you'll have is them bringing a lot of attention during training classes, your patience wearing very thin from their cheeky, intelligent nature; and wearing them out on long walks.
Trust me when I say that I'd recommend them to just about everyone, all they need is patience. I've had other snippy Border Collie owners ramble off to me a list of people who *shouldn't* have Borders, and it upset me when they seem to include practically everyone.
Borders are a wonderful dog and mine have always been good with kids. (Especially my current dog, [I have a few photos of him in my profile,] who adores my nephew, and follows him everywhere like my nephew is a miniature farmer. ) If you can invest a lot of love in them, they're the most devoted dog in the world and you'll have a long, interesting, time spent with them.
I've had Borders for years so I can help with the bathing and grooming question.
It depends on the hair length you get your Border in, they come in short or long. If you go for the long hair, like I have, they need a quick brush at least once a day and a long one every two days or so.
Bathing in summer you can do every two-three weeks, in winter once a month. I towel dry and then use a blow dryer on mine. (It's worth it, they come out so fluffy. ) Be aware in summer though, with a thick coat like they have being a highlander bred dog, they can get dermatitis, but you can take care of that with a store-bought Itchy Wash and anti-itch pet cream.
Border's are very bright and love to outsmart you, but they also love to have your attention and are extremely loyal. If you give them lots of love and games, they'll love you forever.