The Old Testament forbids incest. Does this aspect of the Mosaic law apply to Christians?
Are the Old Testament prohibitions on incest applicable to Christians? - Yes.
Leviticus 18:16 is observed in the Gospel of [Mark 6:17-18], alluding to Christian observance all the Laws in Leviticus 18 regarding incest.
Leviticus 18:16 in regards to Mark 6:17-18 :
Mark 6:17-18 [KJV]
17 For Herod himself had sent forth and laid hold upon John, and bound him in prison for Herodias' sake, his brother Philip's wife: for he had married her.
18 For John had said unto Herod, It is not lawful for thee to have thy brother's wife.
- Leviticus 18:16 [MT]
You shall not uncover the nakedness of your brother's wife. It is your brother's nakedness. (עֶרְוַ֥ת אֵֽשֶׁת־אָחִ֖יךָ לֹ֣א תְגַלֵּ֑ה עֶרְוַ֥ת אָחִ֖יךָ הִֽוא)