Is it permissible to pray behind an elderly Imam whose prayer and recitation are unintelligible, and what are the implications of that?

If the Imam's recitation of Al-Fatiha is correct, and he performs the pillars of prayer, and does not commit anything that invalidates it, and his innovation is not of a disbelief-inducing nature, then prayer behind him is valid. Prayer behind him is better than praying alone at home, even if he is an innovator, as long as his innovation does not entail disbelief. This is based on what Uthman ibn Affan, may Allah be pleased with him, urged when he said: "Prayer is the best of what people do. So, if people do good, do good with them, and if they do evil, avoid their evil."

If there is only one mosque in the village, then praying in congregation behind a sinful person is better than praying alone at home. However, if it is possible to pray behind someone who is not an innovator, that is preferable.

It is permissible to pray in congregation at home, and the virtue of congregational prayer is attained by performing it anywhere. This is better than praying in the mosque behind a transgressor. However, if the Imam does not perform the pillars of prayer, or does something that invalidates it, or his innovation is disbelief-inducing, then prayer behind him is not valid. In such a case, one must pray at home, even if alone.