Contradiction with Genesis 19:24
Genesis 19:24 states that the LORD rained brimstone and fire upon Sodom and Gomorrah, whereas Luke 17:29 narrates that the fire and brimstone rained down after Lot left Sodom, subtly implying an association with Lot's actions.
Genesis 19:24: Then the LORD rained upon Sodom and upon Gomorrah brimstone and fire from the LORD out of heaven;
Contradiction with 2 Peter 2:6
In 2 Peter 2:6, the destruction of Sodom is presented as an act meant to be an example to the ungodly. Luke 17:29 implies immediacy in the destruction correlated with Lot's departure, not explicitly as an example.
2 Peter 2:6: And turning the cities of Sodom and Gomorrha into ashes condemned [them] with an overthrow, making [them] an ensample unto those that after should live ungodly;
Contradiction with Ezekiel 16:49-50
Ezekiel 16:49-50 attributes Sodom's sin and ensuing destruction to more social and moral failings, such as pride and neglect of the poor, without mentioning specific divine intervention as in Luke 17:29.
Ezekiel 16:49-50: Behold, this was the iniquity of thy sister Sodom, pride, fulness of bread, and abundance of idleness was in her and in her daughters, neither did she strengthen the hand of the poor and needy.