We've argued that data profiling is ideally an explorative activity. Data monitoring typically isn't! The measurements that you do when profiling often times needs to be continuously checked so that your improvements are enforced through time. This is what data monitoring is typically about.

Data monitoring solutions come in different shapes and sizes. You can set up your own bulk of scheduled jobs that run every night. You can build alerts around it that send you emails if a particular measure goes beyond its allowed thresholds, or in some cases you can attempt ruling out the issue entirely by applying First-Time-Right (FTR) principles that validate data at entry-time. eg. at data registration forms and more.