First, let's look at the original sentence and break it down:
He left for Mumbai on Sunday arriving there on Monday.
Arriving can either be a present participle or a gerund, based on the -ing ending. Clearly its use as a gerund in this case does not make sense. It does not describe a place from which he may have left, and it does not serve as an appositive for any of the other objects in the sentence. This makes it a present participle. One of the uses of a present participle is use after verbs of movement, action, or position, to indicate parallel activity. This would mean that he arrived at the same time that he was leaving. That is clearly not the case, and so the use of a present participle is invalid in this case. While you may think that the sentence conveys that he successfully arrived, it does not, because it is not consistent with the rules of grammar. Hence the error in it that you were to spot.
The proposed correction is indeed correct, and it does not change the meaning of the sentence, because again, the sentence as it is, is not workable. I will deviate slightly from user3169's intended meaning, in that I would read the corrected sentence as:
He left for Mumbai on Sunday (in order) to arrive there on Monday.
This construction indicates the intended result, not the actual result.
Second, let's look at your proposed change to the sentence:
He had left for Mumbai on Sunday arriving there on Monday.
Arriving is still a present participle in this sentence, so it is still taking place at the same time as leaving. Changing the tense of the main verb does not alter this behavior. So no, this is not better than the original sentence for the purpose of communicating. As user3169 answered, the correct way of communicating this is:
He left for Mumbai on Sunday and arrived there on Monday.
This all matters because you tagged this as an exam question, not as conversational English. You also did not provide any further context, so we have to take the sentence on its own. However, this type of language can be used in the context of transportation, in which case, the method of transportation is assumed. For instance:
Q: Did he arrive here (Mumbai)?
A: Yes, according to our records. He left for Mumbai on Sunday (on a plane) arriving there on Monday.