What is the ruling on swearing by "I swear by that which is unlawful that you will no longer take pictures with a mobile phone," and does this apply to mistaken photography, especially if the wife was menstruating at the time of taking the picture?

The preponderant opinion is that an oath taken by declaring something to be unlawful (al-halif bil-haram) takes effect according to the intention of the one who swore it. If he intended divorce, then it is a divorce. If he intended ẓihār, then it is ẓihār. If he intended an oath (a regular yamīn) or did not intend anything specific, then it is an oath.

If the one who swore the oath breaks it, then what he intended takes effect, and the fact that the wife was menstruating has no bearing.

However, if the wife exposed herself forgetfully or mistakenly, and not intentionally, then there is a difference of opinion among scholars regarding the breaking of the oath. The preponderant opinion is that the oath is not broken in such a case.

Swearing by declaring something to be unlawful is impermissible. The permissible oath is swearing by Allah the Almighty.