Assalamu-alaikum, if someone mistakenly calls their wife their mom, does this have any effect on the nikah?
Zihar is a term denoting a custom of the Arabs in the days of ignorance. In case of disagreement with their wives they used to say to them, “You are for me like the back of my mother.” After saying this, they used to take their wives as their real mother in being prohibited for them, and the ties of marriage were held to have been broken for good. (Maariful Quran p.345 v.8)
Zihar is effected when a man attributes a part of his Mahram’s (mother, sister etc) body which he is not allowed to see (back, private parts etc) to his wife, in that the same way it is unlawful for me to see these parts of my Mahram, you (the wife) is also unlawful for me. (Raddul Muhtar p.123 v.5)
Regarding your question, calling your wife mistakenly “mum” will not have an effecte on your marriage.
Only Allah Knows Best
Mohammed Tosir Miah
Darul Ifta Birmingham