Claim :

 
If the spin of planets, galaxies, etc., came from the fact that the big bang matter was spinning when it blew up, then the conservation of angular momentum demands that all planets be spinning in the same direction. Since some planets and moons spin in a retrograde motion, the big bang is disproved.
Source:
All About GOD Ministries, 2002. Big bang theory. http://www.big-bang-theory.com/

 

BrewYet Answer:

Basically it is saying  if it starting spinning in one direction you should keep spinning in the same direction, 
That is a big law of Physics, but if we follow that logic, then your car would only be able to go in one direction, because once you wheels start spinning they couldn't change rotation.
But we know that if you apply brakes you can stop the spin, and with help of a transmission you can actually make the wheels spin backwards. (its black magic)

I'm not going to say what caused the planet to spin other ways, but if something starts spinning in one direction you can change it to spin another direction. 

This response comes from not understanding the rules of physics.  Basic newtons 1st law:
Every object in a state of uniform motion tends to remain in that state of motion UNLESS an external force is applied to it.

The reason angular momentum gets a special definition is because depending on the point of view, the object could not be in a uniform motion.  So they need make a special explanation for itso it would be true from all points of view.

From Simple Wikipedia:

Angular momentum is important in physics because it is a conserved quantity: a system's angular momentum stays constant, UNLESS an external force acts on it.

Also in Response:

   1. The claim is based on so much ignorance and so many misunderstandings that it is hard to know where to begin.
         - The big bang was not an explosion. Space itself expanded (and is still expanding).
         - The big bang is quite a different subject from the formation of solar systems. Rotations within the universe are not expected to be related to any rotation of the cosmos. Galaxies probably arose from slightly denser regions of the early universe, which coalesced and combined due to gravitational and viscous interactions. Since these early density fluctuations were apparently random, we expect galaxies to have random orientations. Solar systems within galaxies have still different origins and additional random influences on their orientations.
         - Conservation of angular momentum doesn't require that everything spin the same way. It requires that a change in spin in one object be compensated for by an opposite change in spin in one or more other objects. Retrograde planets are not a violation of angular momentum because other bodies in the early solar system could account for the compensating spin.

   2. If the big bang were an explosion, we would expect different spins. When something explodes, pieces fly out spinning in all directions.