From my personal experience, the moment you find yourself writing scrips to clean up data; like cleaning the database every so often, scripts to clean up images, et cetra, you have an architecture that is not scalable.

The second observable sign is when you find yourself adding database columns to hold computed values that are easy to evaluate at application runtime or boolean fields whose states/values depend on other values database values, or when you start accumulating database enums to handle state change.