Should one continue following the program of a foreign person who mistakenly, out of ignorance, put music with the Qur’an, then apologized and corrected his mistake, with a promise not to repeat it? And what should one do if the mistake is repeated?

As long as the program has been modified and the error removed, there is no harm in continuing to follow it, especially since its owner has apologized and promised not to repeat the mistake. If the error recurs unintentionally, and it is rectified and apologized for, there is also no harm in continuing to follow it. What is forbidden is to follow the program while the error exists without it being rectified.