It is not permitted for men or women to look at the mirror in the state of Ihram for checking of make up or hair or beard etc.. But it has no problem in other purposes like looking the sides of the car, or observing the tooth or mouth by a physician, or looking at the mirror without seeing his/her own face, or looking at the mirror for seeing the condition of injuries.
Looking in the water reflection or a polished or glossy object for checking the condition of the face and hair similar things is Haraam in the state of Ihram.
If a Muhrim looks at the mirror involuntarily then there is no problem. However it is better to cover the mirrors of the rooms in which Muhrims are staying there during Hajj in order that they do not look at the mirrors suddenly and involuntarily.
Looking into the glass of a window or eyeglasses from which the other side is visible has no problem.