You're right that the referendum did not legally compel Parliament to this vote, but many MPs thought that it ethically compelled them to it, and for good reason: The entire premise of the referendum was that Parliament would act on the results. The referendum didn't just pop up like a random opinion poll; it was years in the making, came about as a result of political negotiations, and followed a high-profile months-long campaign.
Elections were just held following the Article 50 vote precisely to give voters a second chance to express their view on Brexit, and this resulted in maintenance of a pro-Brexit Tory government.
By "irregularities", you seem to imply corruption in the conduct of the referendum. Which exactly are you referring to? Your link provides no guidance.
First, the famous referendum was advisory, and in no way obligated the government to do anything. Technically it was just slightly serious than a public opinion poll.
Second, the question was too unclear, and it was not clear what will happen in the case of a "leave" vote.
Third, the result was too inconclusive -- a 4% difference is too small to base such strong decisions on, especially after such a short campaign with so many irregularities as this one. [0]
And finally, even if the result required the government to act on it, there was no provision that it has to happen so soon. For a serious "brexit" there should be more time to negotiate and reach a solid deal.
[0] http://www.venice.coe.int/webforms/documents/default.aspx?pd...