and will protect you from any legal stickiness if one of your customers decides to get nasty because your app lost their data or you find yourself on the wrong end of a copyright lawsuit.

Mostly. A corporation is no assurance that a court will not find you personally responsible for damages, perhaps due to (in the court's eyes) negligent or malicious behavior.

That said, you are of course better off with a distinct legal entity but you still have to cover your ass and document responsible behavior (e.g., that you pay bills on time, do due diligence on tools and equipment and hiring, etc.) and that you act in good faith.