It would be great to have a possibility to export integration logs via API or set up advanced filters and alerts on Integration Logs directly in Zendesk.
Currently, the only way to learn about integration error is to manually check https://$domain$.zendesk.com/admin/apps-integrations/integrations/logs page, which is inconvenient operation routine.
It would be better to have some alerts configured (with email notification to selected admins) for error events. Alternatively, it could be just API endpoint to access integration logs, so it can be integrated with monitoring tools (e.g. PagerDuty, OpsGenie).
Use Case / Business Priority
Missing integration errors will result in integrated data inconsistency. In case of customer's data inconsistency (e.g. integration with Salesforce), it ultimately leads to bad experience for the end-customers served through Zendesk products, as agents get wrong data about customer in Customer's profile.