Dating the ex wife
Set aside time for each of them and honor it — don't drag your lover along on girls' night out (not even if your lover is a lady; queer chicks are about this), and don't invite your friend to what was supposed to be a romantic dinner at home. Don't do this ever, but especially not if his last girlfriend is the person you're going rock climbing with Sunday.
No matter what his answer is, it's going to make things weird.
Be clear on what expectations you do have of him or her and of your new relationship. One of the benefits of dating an ex is that the two of you did share good times before you started your new relationship.
In general, allow your friend and your sweetheart to decide how much contact they want with each other, and don't push them to associate if they're not into it.
Save it for your diary or for anyone who didn't date him. This can be extremely tempting if they ended on bad terms and you know you'll find a sympathetic ear.
However, in order to maintain a healthy relationship with both of them, it's crucial that you never seem even a little like you're taking sides in their breakup or casting either one as the bad guy, even months or years after the fact. For instance, if your friend doesn't want to go to parties where her ex will be in attendance, don't pressure her.
In fact, when we met, my now-partner was on a date with my best friend.
They dated casually for a few weeks before they split up and we got together, and three years later the same friend gave one of the readings at our wedding. It's common to assume that anything shared with you is by default shared with your partner as well; however, your friend might be much less comfortable speaking to you in confidence if she thought the details of her personal life were going to be relayed to someone who used to share her toothbrush.