Not a comprehensive list but here are several:

(1) Our health care costs are still about 50% higher on a per capita basis than any other country in the world.

(2) The influx of patients not previously insured has delayed access, especially to specialists. A similar thing happened in Massachusetts after Romney extended insurance to everyone.

(3) There has been no mechanism to prevent the monopolization of hospital services, so we have seen places like Mass General eliminate the competition by buying them, which has the effect or reducing choice for patients and increase costs.

(4) There has never been a truly functional marketplace for health care, and while some of that is endemic to health care itself -- it's not the same walking away from a doctor as it is walking away from a car dealer -- Obamacare has failed to do much to improve that marketplace.

I could go on but I think you get my point. But to borrow a medical analogy, just because a system has many failings does not mean the every remedy will make things better. Bleeding patients was standard until the late-19th century even though that treatment caused more suffering, not less. It is in that sense that I oppose efforts to simple repeal Obamacare simply because it is politically expedient for some to do so. Both the House bill and iterations of the failed Senate offerings would take a problematic health care system and make it worse -- none of those partisan bills would change the core problems in the system and all would reduce access and further inflate costs.