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I thought that the error was C because I thought the comparison should have been:

Because sound waves travel faster in liquids than in gases, the speed of sound in water is greater than that of sound in the air.

Why is the quoted version above incorrect?

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    The quoted version is not incorrect. But the original sentence is not incorrect, either. – Peter Shor Feb 19 '16 at 23:59
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    It seems to me that either E (no error) is the right answer or (owing to a selectively nitpicky question asker) D is the problem because "that of sound" could be replaced by the word "that" alone, since "that" can stand for the entire phrase "the speed of sound." I don't see anything wrong with segment C of the sentence, although I don't see anything wrong with your shorter version of it either. If D is the "correct" answer, you have a bad test question on your hands. – Sven Yargs Feb 20 '16 at 0:00
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A, B, C and D are grammatical. Even taking SvenYarg's comment to your question into consideration, there exists a grammatical interpretation for D.

Your question asked about C in particular. The word they in "than they do" refers to the previously-mentioned sound waves, and do refers to travel. It can be expanded to "... than sound waves travel ...". This phrasing (C) is grammatically correct. (This link provides more examples of similar phrasing.)

E is the correct answer as a meta-statement about the preceding sentence. Alternatively, E is incomplete as a sentence because it's missing a full-stop (and arguably incomplete even with a full stop). Either way, E is the correct answer.

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Both are correct. One's just a more compact and simple way of saying things.

I like apples and I like pears.

I like apples and pears.

Sound waves travel faster in liquids than sound waves travel in gases.

Sound waves travel faster in liquids than they do in gases.

Sound waves travel faster in liquids than in gases.

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