The murder victim being active duty Navy would not make the case the jurisdiction of local police, the homicide case would fall under the jurisdiction of NCIS & JAG. Now if said military victim were killed off of military controlled property, and it appears the suspect is not military, local police can work the case jointly, but they do not have sole jurisdiction.
When Harm prepares to leave the party at the French embassy, he says that he'll get his coat. However, he wears service dress white, the warm-weather formal white suit with a choker collar, which is not worn with another coat (except a raincoat when appropriate). There's no rain on the evening in question, so Harm's line is unrealistic.
The 'laser mic' Harm uses to listen in to the ambassador's wife is emitting a red light. This would draw attention to him. Real laser mics use an invisible infrared beam.
The crime scene in this episode is at Arlington Cemetery and is being investigated by the D.C. police, including uniformed D.C. officers being at scene. Arlington Cemetery is on Fort Myer, a military base and a crime there wouldn't be investigated by civilian authorities, even if it were in D.C., which it isn't. In about 1850 D.C. gave back the land on the far side of the Potomac to Virginia. There is no part of D.C. on the Virginia side of the Potomac, where Arlington Cemetery is, so D.C. police have no jurisdiction there in the first place.
Lt. Austin is at an official diplomatic function, she is there in her capacity as a Naval JAG officer, therefore it is inappropriate for her to be wearing a dress (civilian clothing). She should be wearing her dress whites, just like all the other military personnel present.
The MP sailors guarding the suspect's room door at Bethesda Naval Hospital are wearing the wrong rating insignia. The Petty Officer Third Class on the left is wearing the rating badge of a aviation mechanic, the Petty Officer Second Class on the right is wearing the badge of a torpedoman's mate. The Navy's military police wear the master-at-arms rating, in fact they are technically addressed as master-at-arms, not MP's.