There are a few points that need to be explained in connection with the above question:

1. The meaning of the Prophet's wives being the mothers of the believers: In verse 6 of Sura al-Ahzab, God, the Exalted, addresses the believers as such: "The Prophet is closer to the Believers than their own selves, and his wives are their mothers…"[1] This verse seeks to explain the prohibition of the believers' marriage with the wives of the Holy Prophet (s). Else where the Quran says: "And it is not right for you that you should give trouble to the Messenger of Allah, nor that you should marry his wives after him ever; surely this is grievous in the sight of Allah."[2] This verse does not denote anything more than this.[3]

2. Declaration of the purity of the wives of the Prophet (s) in the Quran: If you mean by the word "pure" in your question absolute and comprehensive purity which is what Ayah of Tathir (purification) refers to, then it relates only to the Holy Prophet (s), Imam Ali (a.s), Fatima (s.a), Imam Hasan (a.s.) and Imam Hussain (a.s.); it does not include the wives of the Holy Prophet (s).

For further information in this regard, refer to Index: Ayah of Tathir (Purification), question 1504 (site: 1557).

As for being pure from charges of indecency, the story of the Ifk (slander) relates to one of the battles of the Prophet (s). According to some reports narrated by Sunni narrators, one of the wives of the Prophet (Aisha or Mariyah Qibtiyah)[4] was also present in the battle. For some reasons, she had fallen behind the caravan. Unfortunately, some hypocrites who had seen the Prophet's wife (in a lonely condition with another man) began to gossip and spread slanderous lies about her. Eventually the story reached the Prophet himself and by then the whole community was talking about what might or might not have happened to her. God rejected this accusation in order to defend the Prophet stressing on the purity of the Prophet's wife from accusation.[5] In the foregoing verse, the Quran stresses on the purity of the Prophet's wives from indecent actions.  This statement is not only defending the purity of the wives of the Prophet (s) but it is also defending the Holy Prophet's honor and respect because such a false accusation deters the prophethood. However, this confession on the part of the Quran does not mean that the Prophet's wives are immune to all kinds of mistakes and errors. They are not infallible in the same way as the Prophet (s) or the Imams because the Quran asks two of the Holy Prophet's wives who had committed mistakes and who had exposed some of the secrets of the Prophet (s) to repent. It says:

"If ye two turn in repentance to Him, your hearts are indeed so inclined; But if ye back up each other against him, truly Allah is his Protector, and Gabriel, and (every) righteous one among those who believe,- and furthermore, the angels - will back (him) up. It may be, if he divorced you (all), that Allah will give him in exchange consorts better than you,- who submit (their wills), who believe, who are devout, who turn to Allah in repentance, who worship (in humility), who travel (for Faith) and fast,- previously married or virgins."[6] 

According to all tafasir (commentary books) of both Sunnis and Shi'ah, these two women (the revealers of the secrets) were Hafsah and Aishah.[7]

These verses clearly speak about these two women opposing the command of the Prophet and about God threatening them to divorce by the Prophet (s). The question is: Given that these two women opposed the Prophet (s) and did what they should not have done, was it not possible that they commit mistakes even after the demise of the Prophet (s)? Is their opposition to Imamate and Wilayah stranger or more weird than their opposition to the Prophet (s)? There is no doubt that all Muslim religions agree that following Uthman's assassination, Imam Ali (a.s) had definitely been the fourth caliph and successor to the Prophet (s). It had been obligatory on all Muslims to obey him. Certainly opposing him and revolting against him amount to opposing and revolting against the Prophet (s). In addition, the Prophet's wives have been commanded in the Quran to stay indoors and to guard themselves against evils[8], are their revolt and participation in a battle against the guardian of the affairs of Muslims in compliances with the Quranic verse?!!

You can study the reasons behind the Battle of Camel (Jamal) by referring to question 158 (site: 1250).