If you look at the download methods for most flash microcontrollers you will find the verify is the accepted method. Usually, once programmed, the lock bits are set so you can't do an external verify. You might want to do verifies at different voltage levels to detect any marginal flash cells.

In days gone by where external eproms were used, there was usually a checksum (not CRC) for each eprom. Part of the startup code would check each eprom's checksum and have some means of alerting the user if there was an error.

In most ECUs for cars they normally have two checksums - one for the code and another for the configuration data and sometimes another for the bootloader if they have this. Again, this is checked at startup.

So, I think I'm confirming what you already know! Verify the data when you load it and check each time you power up. I think it is normally accepted that checksums will pick a gross error whereas CRCs are more likely to pick any error - you choose the level of insurance cover you want and can afford!