Should you use your employer's corporate letterhead to address a personal issue? Why or why not? Could such a practice result in legal or ethical issues?

No, that would be highly unethical and against most business policies. It would be a misrepresentation. Handling a personal issue should be written from the individual, with no association to the person’s employer. Letterhead from an employer should only be used for work-related matters. Many companies require a supervisor’s approval to use company letterhead to avoid misuse and misrepresentation. Depending on the personal matter, it may end up violating laws, placing the person in legal trouble.