I'm a retired Navy officer and "mustang" (prior enlisted Navy E-7).
If it's about a discharge, I can tell you that the only way Kerry would've gotten anything but an Honorable or General would be for him to have been seen either at an Admiral's Mast (non-judicial punishment proceedings) and then administratively separated under less-than or other-than-honorable conditions, or for him to have had formal charges preferred and face either special or general courts-martial.
In the case of a conviction at general courts-martial, Kerry would've basically had a felony conviction on his record. No matter how highly connected he was, there would've been no way to disguise such a black mark.
There might possibly have been some tomfoolery with his discharge status later on in the years after he left the Navy, through the Board of Correction of Naval Records (BCNR). Any servicemember can petition the Board for review and correction or upgrade to a higher-rated discharge of their general through Bad Conduct or Dishonorable discharge.
If this is what happened, then those matters are closely-held, with even a new DD-214 (Certificate of Discharge or Release from Active Duty) being issued to reflect an RE-R1 or RE1 discharge code (the type of code determines your suitability for reenlistment or future retention).
Again, in order for some unfavorable rating at discharge to have occurred, LT(jg) Kerry would have had to have engaged in some behavior in contravention of the Uniform Code of Military Justice, have been investigated for under an Article 32 JAGMAN (Manual of the Judge Advocate General....the legal manual that outlines investigative procedural matters) investigation and then brought to Admiral's Mast or some form of special (but not summary) or general courts-martial.
No Navy Report of Officer Fitness (FITREP) that Kerry has released has shown something like that occurring, but there are very curious gaps in his FITREP history. For officers, in order to be considered for future promotion, assignments and even character of discharge, there can be no such gaps.
Outstanding post 114. Thank you!