Until the evidence came around showing the Universe is actually increasing in the rate of expansion the big bang model worked quite well. It's prediction of a microwave background to the Universe which was subsequently confirmed seemed to make the theory unassailable. This “dark energy' idea that's become the latest trumpeted theory has always seemed like a kludge to me. It's convoluted tinkering of the big bang model to make it stay viable gives me good cause to become skeptical. I'm convinced a better model is just waiting to be discovered.
General relativity also has big problems with black holes. We now know super-massive black holes are an essentially part of every galaxy's core so they can't just be dismissed as rare curiosities. Until theory can explain such monsters without division by zero they shall remain utterly mysterious.