Wow, now that I can see that on my desktop, what a mess. I can say that I have seen worse though.
Depending on the location, inspections may not mean much
Are you sure it's a MWBC? If so, get that taken care of because the neutral is carrying the combined current of both circuits. It may be that the red of one circuit is on the tandem and the black is on either the breaker above or below the tandem. And, it may predate the handle tie rule. I don't remember exactly what edition of the NEC introduced it to us, but it's been fairly recent.
It might have been AFCI "protected" at the time of the inspection. Someone might have come along after the fact and thrown the arc fault breakers in the trash where where they belong. I wouldn't ever do such a dastardly thing, but someone else that cares nothing about the safety of others might.
Also, this probably isn't the case, but the inspector may have not even pulled the cover off the panle. I had an inspector call me up and threaten to fail me for not leaving the panel cover off for a final inspection for and addition once. He claimed that his municipality had a rule that stated they couldn't take the panel cover off, it had to be done by the electrician. I had the homeowner meet him so I wasn't even there. He told me that he would let it go this time, but next time I had better either leave it off or be there for the R&R. That was the last time I pulled a permit in that area.