Is there any problem with a man going into a mikvah that women use without changing the water in between?
Answer:
There is no halachic problem with this practice, although for a number of reasons (halachic and hygienic), it is preferable (and is the common custom in most communities) that the men's mikvah is separate from the women's mikvah.
Sources: See Ein Yitzchak, Orach Chaim 2; Nefesh Chayah 40.
