How to check DB last compilation date

Any time the database compiler is started a database queue processor task is pushed on the database queue. The task logs a warning message to the system journal (table: DialogJournal). Look for the MessageString '#LDS#Processing is disabled (wait for compiler).|' in the table. It might give you the last time (see column MessageDate@DialogJournal) that the system must be compiled. It does not tell, that you might have waited a day before starting the compiler, but combined with the logs of Designer, DbCompiler, Transporter etc you could retrieve the time the compilation finished.