I think it would be interesting to track how many check results of each type (compliance, violation/warning, exception, …) we generate, and show the corresponding graph in Grafana. It would be our own version of https://angryloki.github.io/wikidata-constraint-violations/ (which parses the database reports generated by KrBot, I believe).
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Global count will probably be difficult... for now I think the best we can do is the average number of violations/... per entity, since in the API requests we only have a per-entity view. (Says Lucas writing from Lydia's account :) )