Looks like some flame impingement at the flue opening. Could be a partially blocked cross over vane on the in-shot burner or some other anomaly, like low gas pressure in the manifold. You say you're getting a really good deal on the house and expecting to have to fix up a lot of things isn't something that should be a surprise. Rest assured the heat exchanger has a lifetime warranty if you can convince the wholesaler you've owned the house since the unit was installed. That's the requirement on a "Limited" lifetime warranty. Otherwise, you can run it till it fails and then have a new one, properly sized using Manual 'J' installed for greater comfort.
If YOU want change, YOU have to first change.
If you are waiting for the 'other guy' to change first, just remember, you're the 'other guy's' other guy. To continue to expect real change when you keep acting the same way as always, is folly. Won't happen. Real change will only happen when a majority of the people change the way they vote!