Welcome to PhysicsForums, Force1!
It would be completely misleading to say that Big Bang Theory is wrong ("equations ... don't work") because it does not answer every possible question about physics. There are plenty of open questions about the very early universe, and experiments are underway to answer these as best possible. There is no guarantee that answers will be found to all of these questions. It's not like we can actually re-create those early conditions in the laboratory. The LHC gets us closer, but in terms of the very early universe (10^-43 seconds) it is a far cry away.
If I recall what they are saying in that particular show, they indicate that Einstein's General Theory of Relativity breaks down at that point in the very early universe. This is a true statement, and has little or nothing to do with Big Bang Theory itself. The Big Bang was an initial event and the current theory describes the evolution of the universe subsequent to the Big Bang in many particulars. The theory does NOT attempt to explain the reason for the initial event itself. It is hoped that future science might someday go there (i.e. new theory and experimental evidence to indicate the cause of the BB) but that is speculative.
As to elementary particle masses, I think the observation of the Higgs might answer a lot of open questions regarding the Standard Model. This is an exciting time in physics, and there is a lot of great research going on.