What are some examples of pilot error with criminal negligence?
In the US, negligence would imply willfulness. Errors and accidents don’t imply willfulness nor negligence. That’s the difference between a death caused by an automobile traffic accident due to weather and one caused by a drunk driver. The latter is criminally punishable. The willfulness to do something wrong or not do something right is negligence. Making a decision that an average person would consider reasonable should not be prosecuted. Even if it is the wrong one.

The converse of making a reasonable decision in the case of flying would be to willingly fly the aircraft in a manner beyond the pilots capability or legal competency. If the pilot is not certificated and current, or flying the aircraft into a situation for which it is not certificated could be considered as negligent. The pilot had to do so due to an emergency, that would be a different story.

The same is true regarding intent. If your intent was to break a law, rule, or regulation (even if you did not know there was a law, rule, or regulation regarding your actions), that is criminal. A prosecutor or FAA official can even argue for the criminality of breaking a recommendation, best practice, or commonly accepted procedure if your actions led to an accident, injury, or fatality.