(Note that even the best people are dunderheaded from time to time.) If an application has been deployed to a new environment but its performance is, say, 8x worse or more, ensure that the relevant database indexes are functioning properly. The hardware may be magnificent and the database well-tuned, but a sequential scan of many records will deliver a gut-punch to performance. It's also obviously not well-suited for caching.
Bonus tip: a good database engine has the ability to show the plan/strategy it computes for a query. Start there to find query optimizations that matter.