That will only refer to position i.e. some 25 degrees above the horizon whereas the sentence needs to refer to distance and position. We need to use as instead of that. For the same reason A & B is wrong..
Hope this helps.
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Methinks D is better than E because it maintains a sort of ||ism - 'the comet Crommelin passed the Earth' and 'will (pass) Halley’s comet'. Not sure, but E looks a bit wordy too!
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V.

A is a good catch in this question. But ,that modifies horizon, therefore its wrong.

E doesn't compare the two things correctly. X passed through a position, as Y will do. It's wrong because the second clause is not parallel the first clause.

X passed through the same position, as will Y. is a better structure.

Source of the text in PINK: MGMAT discussion board.

The problem with answer choice E is that, by including the helping verb will, the primary verb pass is already inplied. Thus, answer choice E actually "reads" the comet Crommelin passed the Earth at about the same distance and in about the same position as Halley's comet will do pass the next time it appears. Thus, the verb do is both unnecessary and is not parallel to the verb pass
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Now, Here is MY take on OPTION (A) :
(A) that Halley’s comet will pass

Let's try to understand what the word "that" refer to ?

In its most recent approach, the comet Crommelin passed the Earth at about the same distance and in about the same position, some 25 degrees above the horizon,that Halley’s comet will pass the next time it appears.

Let's remove the modifier that is enclosed within the commas. Remember that when you throw out the modifier, the commas go out the window too.
Voila, the word "that" DOESN'T refer to horizon, instead "that" refers to position.

In its most recent approach, the comet Crommelin passed the Earth at about the same distance and in about the same position that Halley’s comet will pass the next time it appears.

The problem that i have this version of the sentence is that , the word "that" now refers exclusively to position and loses reference to the fact that the "distances" are also being compared. The intent of the original sentence is to compare the similarity in aspects of DISTANCE and POSITON, while the newer version of the sentence only conveys the similarity in the position.

The following excerpt colored in green has been taken from e-gmat blogs.
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Grammatically COMMA + THAT is not correct usage. By definition ‘that clause’ presents required information or essential information and hence cannot be separated from the entity that it modifies by using a comma.
However this does not mean that you can never see a comma prior to that. When you do see comma before that, you will see a comma pair. In such cases non-essential information or additional information will be sandwiched between this comma pair. The sentence structure will look something like this:
Noun,noun-modifier,that clause
In the above structure, comma does not separate ‘that clause’ from its ‘noun’. The complete comma pair is used to separate out the ‘noun modifier’. Lets review this with some examples:
Oprah Winfrey hosts a talk show that has won multiple awards. – Correct
Oprah Winfrey hosts a talk show, that has won multiple awards. – Incorrect
Oprah Winfrey hosts a talk show,considered the highest-rated program of its kind in history, that has won multiple awards. Correct
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Why is E incorrect? I'm still confused.

I got it wrong as A. I went through the MGMAT experts' comment but still couldn't understand completely. So, this is my attempt to independently decipher this question.

In its most recent approach, the comet Crommelin passed the Earth at about the same distance and in about the same position, some 25 degrees above the horizon, that Halley’s comet will pass the next time it appears.

(A) that Halley’s comet will pass
(B) that Halley’s comet is to be passing
(C) as Halley’s comet
(D) as will Halley’s comet
(E) as Halley’s comet will do

Some points to think about:
1) About the same X as Y -- this convention needs to be followed for comparison's sake.
2) The author intends to say that both comets passed through the same location and in about the same position.
3) WILL or WILL PASS are both correct usages in this case. WILL PASS is implied in the case where WILL is used as a standalone.

Note: My feeling here is that you cannot simply use a THAT vs. AS split because THAT by itself is not a problem here. The actual problem here is the main verb PASSED and the comparison verb which is WILL or WILL PASS.

To make a comparison smooth and seamless, the OG advices to have X and Y (two things to be compared) to be as close to the comparator word in this case which is AS.

So, look for the answer choice where the verb comes immediately after the comparator AS. The only option is D. All the other options seem to compare the where the Crommelin PASSED to the HALLEY'S COMET ITSELF. So, you are comparing a location or a point in space to a comet. You can only compare a point in space to either the point itself or another point in space.

Hope that helps!!