Is it permissible for a person to stop praying with the congregation in the mosque if the Imam is someone with whom he has a dispute (religious or worldly), and what is the ruling on congregational prayer behind someone who is believed to be immoral or disobedient?

Disagreements in worldly matters do not justify abandoning congregational prayer, nor do they invalidate the imamate, even if the disagreement pertains to religious matters:

If the Imam is one of the people of innovation (Ahl al-Bid'ah), then the ruling on praying behind an innovator must be consulted for details. If he is not one of the people of innovation, but is rather a fasiq (transgressor), then praying behind him is valid, though disliked, if his transgression is unrelated to the prayer itself. The imams are in agreement regarding the dislike of praying behind a fasiq, and they differed on its validity, but the correct view is that it is valid.

In summary, it is not permissible for the aforementioned person to abandon congregational prayer if the disagreement is worldly, or if it is religious and the Imam is someone behind whom prayer is valid, unless he will find other congregants to pray with.