Play the devil's advocate. Once the person does start revealing the flaws with his or her relationships and all of the problems with his or her partner, the worst thing you can do is to completely agree or to say, "You deserve so much better than that." This will make the person see that you have ulterior motives. Instead, act a bit withdrawn or confused, forcing the person to talk for longer and explain why he or she is really unhappy -- and why his or her partner isn't perfect.
If the person has to explain his or her frustration further and you keep him or her talking, then he or she will notice the problems even more.
Just keep the person talking any time something negative comes up. Questioning his or her thoughts will make him or her explore them even further.
Not criticizing her relationship will also make things better down the line. If you do end up together, no one can tell her that you sabotaged the previous relationship. When you ever openly criticize one of the partners, especially if your plan has failed, it proves you were trying to screw up the relationship.