If the universe started with a 'Big Bang', why arn't all stars the same size and evenly distributed?

This has to do with quantum effects. You are used to the idea, on large scales, that if you do the same thing under the same conditions, the result will be the same. In fact, this is not true, but it can only be seen clearly on small scales. If you are working with quantities (distance, time, energy, momentum) small enough, you will find out that events happen or don't happen according to an intrinsic probability. That is, this probability is not due to our lack of knowledge, as in a poker game, but to the very quality of things. So two occurrences under exactly the same conditions can come out differently. These differences are sometimes called quantum fluctuations. So, in the big bang, when the size of the universe was very, very small, and the time in which things happened were also very, very small, there were a lot of these quantum fluctuations. That means that the distribution of energy, and therefore later mass, was very uneven at first. These effects were then multiplied as the universe expanded. To make an analogy, if you were to aim a rocket at the moon, and your angle was just a tiny bit off at launch, then without course corrections you would miss the moon because the error would become more and more significant as the distance became greater.

Galaxies ARE more or less evenly distributed. Variations from complete smoothness, however, and the very existence of those galaxies, is due to initial "lumpiness" in the Universe. The existence and apparent size of those lumps in the cosmic background radiation was PREDICTED by Big Bang Theorists, and finally observed with the COBE and WMAP space based observations. It is believed to be due to quantum fluctuations that were amplified by Guth's proposed inflationary scenario just after the Big Bang.

All stars didn't form at the time of the Big Bang (in fact, none of them did), and even if they did, why would they all be the same size and evenly distributed? Does that happen with any other kind of explosion? And the Big Bang wasn't an explosion, but most people, including (probably) you, assume it is, so I'm using that comparison.

The universe was not evenly distributed when it formed. Different regions were of a higher density than others. There are two reasons for this:

1- Quantum effects are proabilistic, so there was a random element to where things ended up.

2- A mysterious particle known as the X-boson existed in the early universe. As it cooled, both it and its counterpart, the "Anti-X", decayed to simpler matter and antimatter. For reasons we don't yet know, the anti-X did not produce as many antiparticles as the X-boson, so some particles were spared.

I dare presume you come from a christian fundamentalist stance, so let me put it in a form that can relate to you.

If we are all descendant of Adam and Eve, why aren't we all having the same skin color and evenly distributed?

For the more technical argument, it has something to do with the so called butterfly effect, where the smallest variation in symmetry will amplify itself and cause clumping on a huge scale over time.

All of the above answers are right but the bottom line is everything in the universe is unique.

If you fill a car with dynamite and explode it, why arent all the pieces the same size?

What makes you think they aren't?

Oh, yeah... science. Damn those guys with their hypotheses, experiments and conclusions!

Theories? We don't need no stinkin' theories! We have public opinion on our side!

Because explosions are not evenly distributed

theyre not now but ether way an xplosion wouldnt evenly distribute much