Let's critique the Wiki, one section at a time. This thread tackles the task for:
http://www.theflatearthsociety.org/tiki/tiki-index.php?page=The+PlanetsFirst, let's consider:
Rotoundity
Q. If the planets are round, why isn't the earth?
A. The earth is not a planet.
This answer assumes that the Earth is not a planet. This is a logical fallacy of assuming the result. The Wiki should describe how FEers scientifically determined that the Earth is not a planet.
Next up:
Size and Magnitude
Q. How big are the planets in the FE model?
A. Pretty small.
This answer lacks any quantitative evidence. How did FEer determine scientifically that the planets are "pretty small"? How big is "pretty small"? By not answering the question, FEers demonstrate that they seem unable to answer basic questions about the Cosmos.
Next Up:
Retrograde Motion
Q. Why do the planets retrograde in the sky?
A. Retrograde motion occurs from the fact that the planets are revolving around the sun while the sun itself moves around the hub of the earth.
First, FEers make several more unsupported, at least here in the Wiki, claims:
1) The planets revolve around the Sun.
2) The Sun moves around the hub of the Earth, without defining what they mean by "the hub of the Earth".
3) Retrograde motions occur for all seven planets.
4) The Sun's motion causes the retrograde motion.
Let's review these in order.
1) No, in FET the planets do not revolve around the Sun as the diagram indicates. The planets do pass over and under the Sun, and not in a circle in the plane parallel to the Earth's surface.
2) Again, FEers makes another unsupported claim. They need to show us how they know that the Sun revolves around the hub. They need to tell us where the hub is. For example, how do they know that the North Pole is at the center of the hub and not the South Pole? Is this, like so many other claims, just wild speculation?
3) No, only the outer planets are seen to move retrograde. Mercury and Venus don't. So the Wiki fails miserably. Why would the inner planets not move in retrograde? Why would Mercury and Venus have phases? Since RET predicts the retrograde motion for the outer planets, since RET explains the reason for the motion (The Earth is overtaking the planet as its orbit is smaller and completed more quickly.), predicts when and where the retrograde motion will occur, and predicts the phases of the inner planets, FET fails miserably.
4) No, the observed motion does not match the explanation. Clearly no one considered that planet in retrograde motion is nowhere near the Sun and is not executing a tight circle about the Sun when it's in retrograde.
Finally, let's critique this statement:
Several retrogrades a year would be more appropriate, depending on the planet.
Again, this is miserably wrong. No planet has even one period of retrograde motion each year. Obviously no one even researched the concept before trying to 'make up' an explanation. How very sad!
Clearly this section was poorly thought out and fails miserably.