Is the congregational prayer invalid if there is one woman that is in prayer with the congregation that is not wearing her hijab properly such that her hair shows?
In all cases, the prayers of the men in the congregation are unaffected. If the woman did so intentionally, knowing that her hair was showing then those connected to her in the congregation from the women will not be considered to be praying in congregation. However, if she were unaware and her actions were not intentional then the congregational prayer is in order.