I'm a Project manager now but spent many years as part of an IT support team for a reasonably large Telecoms software company.
What I can't seem to get my head around, is how all these different post offices were each reporting very similar issues and them not being linked early doors. Did the Horizon customer support team leader not have some kind of daily (or at least weekly) team standups, reviewing each other's open tickets? Trust me, these types of ticket reviews are standard on helpdesks. Were the postmasters even able to actually log a support ticket or were they just handled on the fly by 1st line support staff (The switch it on/off off brigade)
As Rob and Andy rightly pointed out. Every IT system has bugs, always have, and most probably always will. The key is, how quickly you identify, prioritize, and then escalate these issues. If the software devs didn't know about the issues then they couldn't have done anything to fix it.
You identify, escalate, fix, then apologize to your customer for any inconvenience caused and move on.
What jumped out at me on the drama, was how sketchy the support process was. I'd be curious to know how the support process was in real life for the Horizon software.
How the PO auditors and suchlike reacted is a whole different conversation altogether though.