The Prophet, peace be upon him, said:
‘The imam is appointed to be followed as a leader, so do not oppose him.”
[Muwatta Hadith 3.61]

Abu Hurairah reported that the Prophet, upon whom be peace, said,
“The imam is a guarantor, and the caller to prayer is one who is given the trust. O Allah, guide the imam and forgive the caller to prayer.”

An Imam can be replaced.  However, while he is in the position he is, he should be obeyed, except that he should never be obeyed in the instruction to do the haram (prohibited in Islam).

Who is the Imam?

Ash-Shaafi’ee, rahimahullaah, said

“Knowledge is not what is memorised, but what benefits.”

[Reported in Hilyatul-Awliyaa’ of Abu Nu’aym (9/123)]

The following is from Fiqh 2.56a:

The imamate of all the following is acceptable: a discerning boy, a blind person, a standing person for those who are sitting, a sitting person for those who are standing, a person praying fard for people who are praying nafl, a person praying nafl for people who are praying fard. Likewise, a person who has performed ablution can be imam for people who have performed tayammum, as can be a person who has performed tayammum for people who have performed ablution, a traveler for the resident, a resident for the travelers, and a less qualified person for people who are more qualified.

‘Amr ibn Salamah led his people in salah while he was six or seven years old. The Messenger of Allah sallallahu alehi wasallam twice appointed Ibn Umm Maktum, a blind man, to lead the people of Medinah in prayer. The Messenger of Allah, during his last illness, prayed behind Abu Bakr in a sitting position. And he prayed in his house in a sitting position while those behind him were standing. He pointed to them to sit and when he had finished the prayer he said: “The imam has been appointed to be followed. If he goes into ruku’, then make ruku’. When he raises his head, raise your head. If he prays sitting, then pray sitting behind him.”

Mu’adh would pray ‘isha with the Prophet sallallahu alehi wasallam and then return to his people and lead them in the same prayer, it being nafl for him and fard for the others.

Muhjan ibn al-Adra’ reports: “I came to the Messenger of Allah in the mosque and they prayed and I did not. He said to me: ‘Why didn’t you pray?’ I said: ‘O Messenger of Allah, I prayed in my place and then came here.’ He then said: ‘When you come [to the mosque], pray with them and make it supererogatory.“‘

The Messenger of Allah saw a man praying by himself and said: “Who will give charity to this person by praying with him?” ‘Amr ibn al-’Aas led others in prayer when he had made tayammum only and the Prophet approved of it.

The Prophet sallallahu alehi wasallam, after the conquest of Makkah, led the people in prayer by praying two rak’at (except for maghrib) and said: “O people of Makkah, stand and pray the last two rak’at as we are travelers.”

If a traveler prays behind a resident, he must complete the whole four rak’at even if he only prayed part of a rak’ah behind the resident imam. Ibn ‘Abbas was asked: “Why is the traveler to pray two rak’at if he prays by himself and four rak’at if he prays behind a resident?” He answered: “That is the sunnah.” In another version, Musa ibn Salamah said to him: “If we pray with you, we pray four rak’at otherwise we pray two?” He told him: “That is the sunnah of Abu al-Qasim [the Prophet].” This is related by Ahmad.

Do not ask to be the imam, but do be open to it if asked.

Hadith - Sahih Al-Bukhari 8.715, Narrated Abdur Rahman bin Samura
Allah’s Apostle peace and blessings of Allah be upon him said, “(O ‘Abdur-Rahman!) Do not seek to be a ruler, for, if you are given the authority of ruling without your asking for it, then Allah will help you; but if you are given it by your asking, then you will be held responsible for it (i.e. Allah will not help you). And if you take an oath to do something and later on find another thing, better than that, then do what is better and make expiation for (the dissolution of) your oath.”

A man of any race, rich or poor, handicapped or not - who is knowledgeable in Islam, ruling according to Quran and Sunnah - should be obeyed.

Hadith - Sahih Muslim 2977, narrated Umm al-Husayn
She (further) said: Allah’s Messenger peace and blessings of Allah be upon him said so many things, and I heard him saying: If a slave having some limb of his missing and having dark complexion is appointed to govern you according to the Book of Allah the Exalted, listen to him and obey him.

Praying behind deviants in the deen

Narration - Reported by ‘Abdullaah ibn Ahmad, as the saying of his father, Imaam Ahmad, in as-Sunnah (nos.4-5)

The five daily Prayers must be prayed behind anyone [muslim] except a Jahmee, since he denies (all of the attributes of Allaah).  If you have prayed behind him, repeat your Prayer.  On the day of Jumu’ah (friday sermon), if your Imaam is a Jahmee and he is a ruler, pray behind him, (but) repeat your Prayer.

Female Imams?

A woman may be appointed to lead other women in prayer. A woman may make the iqamah or adhan (call to prayer) if no non-mahram men can identify her voice.

Fiqh 1.104a

Said Ibn ‘Umar, “There is no adhan or iqamah for women.” (Related by al-Baihaqi with a sahih chain.) This was the opinion of Anas, al-Hassan, Ibn Sireen, an-Nakha’i, al-Thauri, Malik, Abu Thaur and the people of “juristic reasoning.” Ash-Shaifi, Ishaq and Ahmad said if they make the iqamah and adhan, there is no problem. It is related from ‘Aishah that she would make the adhan and iqamah and lead the women in prayer, standing in the middle of the row. (Related by al-Baihaqi.)