A problem with the simplistic Big Bang theory having to do with the smoothness of the Universe. The Early Universe should have been very random in terms of the temperature and density of different parts of space. This randomness should not have had time to distribute itself more evenly. Yet, this is what is observed in the Universe. The theory of Inflation solves this problem.
Come, you lost Atoms, to your Centre draw,
And be the Eternal Mirror that you saw:
Rays that have wander'd into Darkness wide,
Return and back into your Sun subside.
From Farid al-Din Attar's
The Conference of the Birds