From the article at http://fishdontwalk.com/aviewer.asp?i=8, let's look at some of the statements:

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'The Bible says, "God created the moon to be "the lesser light that rules the night"'.

So why does it spend 50% of its time in the daytime sky? Hardly seems an efficient way to "rule the night".

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'Our moon is 100 times larger than the average sized moon in our solar system.'

Very misleading statistic, considering how small a body can count as a moon. A moon is simply a object in a reasonably stable orbit around some larger non-stellar object. This object described in this link is considered a moon, and is only about a one mile across.

http://www.inconstantmoon.com/lim_0008.htm

The biggest moon is Ganymede, which orbits Jupiter. It is 3280 miles in diameter, compared to our Moon at 2140 miles. The next two largest moons of Jupiter are Callisto at 3000 miles, Europa at 1950 miles.

The largest moon of Saturn is Titan at 3200 miles.

So there are at least three other 'moons' similar or larger than our Moon, the largest being more than 50% larger in diameter. This statistic seems to me somewhat more appropriate in setting our moon in context. Our Moon does have the honour of being by far the largest satellite in proportion to the size of it's parent body (the Earth) of the satellites of the other planets (excluding Charon the moon of Pluto, a 'planet' which is itself is smaller than our Moon), at least.

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'The Bible in Genesis 1:14 says the moon was also created "for signs and seasons and days and years."'

So why does the moon go round the Earth 13.36 times while the Earth goes round the Sun once? Surely if it was set in position to be a convenient timer it would have been trivial for the creator to make it a nice exact number, so the full moon would occur on the same days in the same season every year?

'The gravity of the moon directly causes a bulge of ocean water on the side of the earth toward the moon.'

Actually it also causes a similar bulge on the side of the Earth opposite the Moon, which is why high tides occur almost twice a day. The description of tides in this article is very crude and inaccurate.

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Regarding the Origin of the Moon, the current dominant hypothesis is the Giant Impact theory.

From http://en.wikipedia.org/wiki/Giant_impact_hypothesis:

"According to the hypothesis, 4.533 billion years (4.533 Ga) ago, shortly after the formation of the Earth, a Mars-sized planetesimal hit the Earth at an oblique angle, destroying the impactor and ejecting most of that body along with a significant portion of the Earth's felsic-rich mantle out into space. Some of this material then coalesced into the Moon from an orbiting ring of debris. Current estimates based on computer simulations of such an event suggest the spherical shape of the moon was attained between one and one hundred years after the impact."

This has been supported by computer simulations, the chemical composition of moon rocks brought back by Apollo Missions, and estimates of the size of the Moon's core from seismometers on the Moon.

There is plenty of evidence in the form of large craters on various bodies in the Solar system of large impacts, including on the Moon itself, with reasonable expectation that in the very early history of the system the impacts were much more frequent. Those bodies in more eccentric orbits were much more likely to be involved in collisions, which would have severely changed their orbits or even destroyed them, until gradually the remaining major objects were those in relatively circular orbits as we see today. Of course there are still a lot of smaller objects on very eccentric objects, the debris from these earlier major collision events. The largest collision observed in recent years was the collision of Comet Shoemaker-Levy 9 with Jupiter in 1995, creating a succession of fireballs in Jupiter's atmosphere hundreds of kilometres across. So much for the absence of "catastrophies", "which [have] never been observed in this orderly solar system".

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"it is extremely unlikely fragmented masses formed a single mass".

There is this force called gravity, which the writer appears not to understand, which can cause precisely this to happen, if the total density of debris is large enough. The calculations are tricky but modern computers allow us to perform the calculations fast enough and accurately enough to show that this will happen for plausible ranges of debris density, and once the particles accumulate into a sufficiently large body, it will be pulled into a spherical shape by gravitational forces.

Particles travelling at less than escape velocity, about 7 miles/sec in the immediate proximity of the earth would not have "escaped its gravitational field entirely", they would go into some sort of orbit around the Earth. Those in very eccentric orbits would at some point hit the earth, others would remain in less eccentric orbits, occasionally colliding with other particles or maybe the growing moon. This process of elimination of eccentric orbits in a cloud of particles is what has lead to the rings of Saturn. These conditions lead to the closest we get to "a perfect orbit". Most other objects in the Solar System have anything but "perfect orbits". The orbit of the moon is inclined at about 5 degrees to the plane of the Earth's orbit, and maximum distance from the Earth is about 10% greater than it's minimum distance, hardly "a perfect orbit with earth".

EDIT: minor typos and clean-up