Word describing the one flaw in an otherwise perfect crime, plot or plan

Solution 1:

Consider,

chink [in the armor]

: a weak spot that may leave one vulnerable.

M-W

fly in the ointment

A detrimental circumstance or detail; a drawback.

American Heritage® Dictionary of the English Language

wrench in the works

a spanner (or North American monkey wrench) in the works

A person or thing that prevents the successful implementation of a plan.

Oxford Dictionaries

It was the first chink in the armor, a tiny wrench in the works of their mutual manipulation.

Termination Orders

Solution 2:

Perhaps Achilles' heel (with or without the apostrophe)

An Achilles heel is a weakness in spite of overall strength, which can actually or potentially lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.

Wikipedia

Solution 3:

Two possibilities, hitch or catch.

To illustrate the first, recall that the German plan to defeat the French in 1914 required the Germany army to overcome resistance in the Low Countries quickly. Unexpected Belgian resistance on 5 August required the Germans to spend 11 days to capture the defenses at Liège. From Leadership In Conflict by M Hughes and M Seligmann:

Following this first hitch in the plan, the last of Liège's concrete and iron forts was finally taken on 16 August, and the next day, two days later than planned, the German right wing could proceed with its enveloping move through Belgium and into France.

Quite the hitch, too. The delay meant that the Germans were never able to execute an envelopment of French forces, leading to the bloody stalemate of trench warfare.

To illustrate the second possibility, we return to history, this time post-World War II, 1954 to be exact, when the Egyptians wanted British forces to leave the Suez Canal zone so that Egypt could gain sovereignty over the Canal. So the Egyptians negotiated a settlement whereby the British troops went to Cyprus, and the ownership of the canal was transferred to the Suez Canal Company, which had built the Canal in 1869. That sounds like it would have been a good plan to reduce British influence but as noted in Britain in the Modern World by J A Cloake:

The catch was that the largest shareholder in that company was Britain.

Which pretty much undid this plan to remove British influence.