This is a completely fair question, but actually a difficult one to answer. The 'problem' is that there are a great many contingencies that have to come together to generate a severe contradiction. That's how good Big Bang theory seems to be. It is like asking for 10 things that contradict quantum mechanics.
General relativity predicts how gravity and space-time operate.
If it is found that GR is incomplete as a classical theory, then Big Bang could be doomed because all current cosmological solutions or 'models' are based on solving Einstein's original, general relativistic formula for gravity. In the next few years, a completely new test of GR will happen which will search for 'gravito- magnetism'. If it is not found, GR is in severe trouble, and so will be Big Bang theory. A basic feature of Big Bang theory is that the universe has a specific age given its expansion rate. As you know, the ages estimated for the oldest known stars are between 12 and 17 billion years, however if the Hubble Space Telescope estimates for the local expansion rate are correct, an age for the universe closer to 12 billion years is predicted.