Many flip-flops can be fairly stiff soled. This can reduce the range of motion of the foot. It also will put pressure on the top of your foot at the instep where the flip-flop straps put pressure against your foot when you walk.
Without anything in the back to keep the rear sole of the flip-flop from staying close to your foot, it tends to hang in the back and drag on the ground.
To reduce the chance of your flops falling off and to minimize the aforementioned dangling sole (at the heel), people tend to grasp the front of the flip-flop. This isn't a natural motion — typically your toes point to the sky (dorsiflex) when you walk. This is probably one of the biggest problems with flip-flops because prolonged wear will reprogram your foot to do this grasping thing with every step. Since this would be a bad way to walk barefoot (likely resulting in stubbed toes), well, it's a consideration in opting to wear flip-flops.
You can't really run in flip-flops very well and you certainly can't run in them naturally.
Something else to think about, they can also expose your feet to bacteria and fungal infections. Plus, there is a lack of arch support" and they are flat and typically lacking in a lot of cushion (though there are certainly plenty of foam-soled flops with a fairly plush ride).
They're dirt cheap and pretty minimalist. I can't call flip-flops "minimalist" or "barefoot" in the "minimalist/barefoot shoes" sense because they alter natural bio-mechanics in non-significant ways (The toe grasping thing really seems like an issue to me).
Without much sole, you get fairly good contact with the ground. The lack of support and cushioning encourage a lighter step. In the second article above, this reference jumped out at me: "[Flip-flops] can help with arthritic joints. A recent study conducted at the Rush University Medical Center in Chicago, Illinois, found people who had arthritic knees had less stress on their joints wearing flip-flops than other types of shoes." What the what?
They're super airy! Feet like to breath like the rest of your skin.
They aren't supportive — mostly. There are some fairly overbuilt, heavy, and arch-support/toe-springy flip-flops or thongs out there, so this certainly doesn't go for all flip-flops.
They let your toes splay. No toe box means unconstrained toes.
They're crazy easy to put on and take off. Who doesn't love this aspect of flip-flops?