What should I do if I enter the mosque to pray the obligatory prayer and find someone who mispronounces some letters preparing to lead the prayer? Should I leave, or pray individually behind him, or pray in a mosque further away? And does the ruling of congregational prayer still apply to me in this situation?

The significant error that affects the validity of prayer is that which occurs in Al-Fatiha, not in other surahs. So, if the Imam does not pronounce the letters Dhā (ظ) and Thā (ث) correctly, neither his prayer nor the prayer of those behind him is invalidated. However, replacing the letter Dhāl (ذ) with Zāy (ز) in Al-Fatiha is impactful, and it is not permissible for someone who recites well to follow such an Imam, though some Hanafis have held that it is valid.

If you enter the mosque and find this Imam, you can pray behind him with the intention of praying alone, only outwardly conforming to him. Some jurists have explicitly permitted this. Al-Zarqani mentioned that in this scenario, the intention of following the Imam is not a condition, and one's prayer is valid without it. This applies to someone who knows of a defect in the Imam's prayer.

As for praying alone at home, those who consider congregational prayer obligatory in the mosque only impose it on those who hear the call to prayer. If you doubt whether you can hear the call or not, the default is the exoneration of your responsibility. The majority of scholars do not consider congregational prayer in the mosque obligatory, and for them, it can be performed anywhere. So, if you pray at home, be sure to pray it in congregation with your family.