Of course a lot depends on how close you are to this friend, how long it’s been since they dated, how close their relationship was, and what lingering feelings there exist now. Since I can’t possibly answer every situation, let’s look at what the possible character implications are in the worst-case scenario.
Character: It’s possible that your partner is showing an uncaring side. They may simply not care about whose feathers they ruffle by dating you. It could also reveal dishonesty. Perhaps they still have lingering feelings for your friend, and are dating you to indirectly retread old territory. It certainly brings up possible respect issues, because there are some unspoken rules about dating an ex’s friend, and violating them is possibly an act of disrespect. And lastly, it’s possibly irresponsible, since it could lead to a split between you and your friend.
That’s a lot of possible character issues, but the keyword is “possible”. Like I said at the beginning, it depends on the actual specifics of the relationship. I would see to what extent your potential partner is careful or aware of the delicate situation. If they’re brazen about it, then watch out, they will likely be careless with your heart down the road.
Chemistry: It’s possible that chemistry could also push you away in this situation. There’s a saying, “Don’t shit in your backyard,” and so the relationship could end up stinking if it feels like you’re dating too close to home. Or it could be irritating if the topic of conversation always returns back to your friend, or if dating your friend’s ex creates an awkward love triangle. You may want to let this dimension play out, though, as you may have your own unique chemistry with this person.