Saying that they are the only true Christian church with true apostolic succession.
As far as I understand it, that is mistaken on two counts:
First, because the Mormons believe that the Church apostasized after the death of the apostles and became the “Church of the Devil.” Mormonism then claims that the true church was restored through the Prophet Joseph Smith in the 1820s. Their belief that the Church was utterly lost in damnable error for some 1500 years would make a claim of unbroken apostolic succession impossible (some Mormon correct me here if I've got that wrong);
Second, the Catholic church argues that the Catholic and Orthodox churches --- which together would account for approx. 70% of the world's Christians--- have unbroken lines of apostolic succession.
Hence, it follows that most Christian churches have an unbroken line of succession..