You could approach data quality testing as if you're testing another piece of software by writing tests. We use dbt and it makes writing tests against models (think tables in a db) very easy.
For example, if you have a regional_orders table. You write tests in SQL to test your assumptions about that data:
* I expect regional_orders table to contain no duplicates entries.
* I expect regional_orders to ship to only a specific region.
* So on...
This has worked fairly well so far for me. But are these kinds of tests sufficient? Am I missing something?