Your ex starts dating
And don't ever use jealousy or insecurity over their past relationship to excuse irrational or controlling behavior on your part. It may be tempting ask your friend to analyze what happened between the two of them so that you can avoid making the same mistakes, but resist that urge.
Queers don't tend to expect our dates to come into our lives completely free of prior complication.
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.
This rule is almost never stated or enforced among queer communities.
If you're gay, you will almost inevitably date a friend's ex at some point.