What are the dangers of your PS3 shutting down when it's not supposed to?
Firmware are small bits of programs that internally control all the other pieces of hardware on the device. If a firmware update is interrupted, then you run into the high risk of turning your device into a 'brick' and thus make it very hard, if not impossible, to repair.
Its often okay to interrupt the process when installing games/patches, most software is smart enough to recognize an interruption and either continue where it left off, or restart the process. Worst case scenario, you have to reinstall the game, not a huge loss you can't recover from.
Interrupting saving a game can result in corrupted save game files, which means that you will lose all your progress unless you have backups.
In summary, there is a reason why that message is there. Unfortunately, its getting longer and longer, but its necessary. Try to avoid interrupting any of these as much as possible as you'll lose a few hours of your life reinstalling games at best and completely destroy all your progress in a game or breaking your hardware in the worst case.