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There ARE in fact several serious fundamental problems with the standard Big Bang model.

They are as follows...

Problems with the Big Bang

The hot big bang theory has been extremely successful in correlating the observable properties of our Universe. However, there are some difficulties associated with the big bang theory. These difficulties are not so much errors as they are assumptions that are necessary but that do not have a fundamental justification. The required discussion is technical, so we will be content with a rather superficial statement of the three basic problems that are associated with the big bang and how they might be cured by a new idea that arises from considering the implications of elementary particle physics for cosmology.

The Horizon Problem
We have already encountered the horizon problem in conjunction with the discussion of the cosmic microwave background: when we look at the microwave background radiation coming from widely separated parts of the sky, it can be shown that these regions are too separated to have been able to have ever communicated with each other even with signals travelling at light velocity. Thus, how did they know to have almost exactly the same temperature? This general problem is called the horizon problem, because the inability to have received a signal from some distant source because of the finite speed of light is termed a horizon in cosmology. Thus, in the standard big bang theory we must simply assume the required level of uniformity.

The Flatness Problem
The experimental evidence is that the present Universe has very low geometrical curvature in its spacetime (it is nearly flat). Theoretical arguments that are well established but too complex to go into here suggest that this is a very unlikely result of the evolution of the Universe from the big bang, unless the initial curvature is confined to an incredibly narrow range of possibilities. While this is not impossible, it does not seem very natural.

The Monopole Problem
The only plausible theory in elementary particle physics for how nuclei in the present universe were created in the big bang requires the use of what are called Grand Unified Theories (GUTs). In these theories, at very high temperatures such as those found in the instants after the Universe was created the strong, weak, and electromagnetic forces were (contrary to the situation today) indistinguishable from each other. We say that they were unified into a single force. Although there is as yet no certain evidence for the validity of such theories, there is strong theoretical reason to believe that they will eventually turn out to be essentially correct. Our current understanding of elementary particle physics indicates that such theories should produce very massive particles called magnetic monopoles, and that there should be many such monopoles in the Universe today. However, no one has ever found such a particle. So the final problem is: where are the monopoles?

http://csep10.phys.utk.edu/astr162/lect/cosmology/bbproblems.html

Re: There ARE in fact several serious fundamental problems with the standard Big Bang model.

Moreover, the supposed "cure" to 'fix' the standard BB theory (ie, Inflation theory) is even more flawed than the BB...

The Inflationary Universe

The preceding problems with the big bang can be alleviated all at once (at least in principle), by a new kind of cosmology called the inflationary universe.

The Theory of Inflation

In the corresponding theory of inflation, the Universe, because of properties of elementary particles not accounted for in the standard big bang models, expands for a fleeting instant at its beginning at a much higher rate than that expected for the big bang. This period, which is called the inflationary epoch, is a consequence of the nuclear force breaking away from the weak and electromagnetic forces that it was unified with at higher temperatures in what is called a phase transition. (An example from everyday life of a phase transition is the conversion of ice to liquid water.)

This phase transition is thought to have happened about 10^-35 seconds after the creation of the Universe. It filled the Universe with a kind of energy called the vacuum energy, and as a consequence of this vacuum energy density (which plays the role of an effective cosmological constant), gravitation effectively became repulsive for a period of about 10^-32 seconds. During this period the Universe expanded at an astonishing rate, increasing its size scale by about a factor of 10⁵⁰. Then, when the phase transition was complete the universe settled down into the big bang evolution that we have discussed prior to this point. This, for example, means that the entire volume of the Universe that we have been able to see so far (out to a distance of about 18 billion light years) expanded from a volume that was only a few centimeters across when inflation began!

Solution of the Problems of the Big Bang by Inflation

If this inflationary epoch really took place, it could cure all the problems of the big bang mentioned above. Briefly,

The tremendous expansion means that regions that we see widely separated in the sky now at the horizon were much closer together before inflation and thus could have been in contact by light signals.
The tremendous expansion greatly dilutes any initial curvature. Think, for example, of standing on a basketball. It would be obvious that you are standing on a (2-dimensional) curved surface. Now imagine expanding the basketball to the size of the Earth. As you stand on it now, it will appear to be flat (even though it is actually curved if you could see it from large enough distance). The same idea extended to 4-dimensional spacetime accounts for the present flatness (lack of curvature) in the spacetime of the Universe out to the greatest distances that we can see, just as the Earth looks approximately flat out to our horizon. In fact, the inflationary theory predicts unequivocally that the Universe should globally be exactly flat, and therefore that the average density of the Universe should be exactly equal to the closure density. It is this prediction that we alluded to earlier when we said that there were theoretical reasons to believe that the density of the Universe was exactly equal to the critical closure density.
The rapid expansion of the Universe tremendously dilutes the concentration of any magnetic monopoles that are produced. Simple calculations indicate that they become so rare in any given volume of space that we would be very unlikely to ever encounter one in an experiment designed to search for them.

As if this were not enough, the theory of inflation also presents an unexpected bonus.

A Bonus: Density Fluctuations as Seeds for Galaxy Formation

In addition to (potentially, at least) solving the preceding problems of the big bang, the theory of inflation presents a bonus: detailed considerations indicate that inflation is capable of producing small density fluctuations that can later in the history of the Universe provide the seeds to cause matter to begin to clump together to form the galaxies and other observed structure. See the subsequent discussion of structure growth in the Universe.

Problems with Inflation

Although inflation has many attractive features, it is not yet a proven theory because many of the details still do not work out right in realistic calculations without making assumptions that are poorly justified. Probably most cosmologists today believe inflation to be correct at least in its outlines, but further investigation will be required to establish whether this is indeed so.