Is it better to pray in a more distant mosque if the imam is a beginner and makes many mistakes, and is the prayer valid behind an imam accused of wickedness, but whose guilt has not been proven?

There is no harm in going to a distant mosque if the Imam of the nearby mosque does not recite well, especially if his mistakes invalidate the prayer, such as an error that changes the meaning in Al-Fatiha. If he cannot be replaced, prayer behind him is not valid except for someone who is equally unable to recite correctly. However, if the mistakes are in parts other than Al-Fatiha or are due to poor memorization despite good recitation, then prayer behind him is valid. Prayer behind a fasiq (transgressor) is valid, though disliked, according to the preponderant opinion.