It's speculation on my part, but I'd have to guess that a dishonorable discharge would prompt further inquiry into the person's background.
I think that's part of it, since one of the questions is whether the applicant has been dishonorably discharged within the past five years.
But also, Title 25 M.R.S.A., Sec. 2003, Subsection 1, Paragraph E, Subparagraph (5) [I think that's how it goes] says in part: "The demonstration of knowledge of handgun safety to the issuing authority may not be required of any applicant who holds a valid State permit to carry a concealed firearm as of April 15, 1990 or of
any applicant who was or is in any of the Armed Forces of the United States and has received at least basic firearms training. [Italics mine.]
I don't recall how long it took me to get my first resident permit, but it didn't seem to take very long. I guess having the Small Arms Expert Marksmanship Ribbon showing on both my DD214's, and Security Specialist/Law Enforcement Specialist/Law Enforcement Supervisor for my Primary and Duty Specialty Codes convinced the selectmen that I was probably "okay."
BTW, Subsection 12 of Sec. 2003 says "The issuing authority, as defined in this chapter, shall issue or deny, and reply in writing as to the reason for any denial, within 30 days of the application date in the case of a resident of 5 or more years and
within 60 days of the application date in the case of a nonresident or in the case of a resident of less than 5 years. If the issuing authority does not issue or deny a request for a permit renewal within the time limits specified in this subsection, the validity of the expired permit is extended until the issuing authority issues or denies the renewal." [Italics mine.]
One more reason I'm glad to be out of Taxachusetts.