The absolute worst case scenario (and I've never ever heard of this happening to a cat) is that you could shoot into a vein which from reading about it in humans causes an almost instant BG crash. Again, I've never heard of someone doing it to a cat although I suppose it's theoretically possible - though only if you shot straight into the cat without lifting the skin first. Cats make sub-Q shots easy since their skin is so lose.
Far more likely is just a little cut from the needle. And beyond that, I'm not sure. Those are the only two things I've read about that would cause blood around the injection site. And again - the first one I've only read about pertaining to humans.