I think that if Burke is the one to find the video, he would use that to get out of his marriage. The only reason he's not divorced yet is his ego and the fact that he didn't do a prenuptial contract so he would lose most of his assets to Jade, if not ALL because of the cheating. The video would be the perfect weapon to get out of that.
Now if Cathy finds the video we could have a lot of fun outcomes~ She would probably confront the MC first, then she would jump into the act more directly than ever, knowing that one of her best friends and a compromissed teacher is already doing it. It could possibly open some route for a Cathy/ Jade threesome too.
Now... if Jade finds the video it would be hell on earth for the MC, she would probably try to get back at him and we've found that Jade knows how to hold a grudge and against a student? She has no limitation like with Burke (the limitation being Tybalt). It would be dreadful...
P.S. Now that i'm speaking of that, does Jade has more than one kid? I remember her saying she stays in her 'marriage' for the sake of her kid or son or kids, i don't remember how she says it, could she possibly has more than one? If someone remembers the scene, please clarify.