When is it appropriate to salute indoors?

AR 600-25 is not going to give you the answer on this. Army Regulations don't really apply to Naval Drill & Ceremonies.

You want the USMC Drill & Ceremonies Manual MCO P5060.20

1) Marines don't salute indoors.
2) We "generally" don't wear covers indoors, unless under arms (in possession of a weapon or on duty which is "figurative" armed).
3) The Marine in question is likely conforming to the Event: Cover on for appearances, but Gloves off (if we're outdoors in Blues gloves are on, if we're inside gloves are off).
4) The Anthem/Ensign rates a Salute or going to Attention, however, simply going to Attention would not "visible" on a stage, so rather than violating 1), he placed his hand on heart while at Attention which is a reasonable compromise.

So, he may have some "technical" errors but he maintains the Spirit of our (Naval Services) order in Priority and Protocol. No strict violations that I can see from the picture.

EDIT: Capt Joseph Olson Makes a GREAT point that there was "possibly" (I would say LIKELY) a Public Affairs/Information Officer there and this is a "Staged" Event, and the Marine had some "Directed" Actions.

The Location on the stage makes it "impossible" to face the Ensign (which is displayed on the screen), and "difficult" to face the Music to render Honors (without becoming a distraction to the Performer). This goes back to 3) Conforming to the Event.

During Bush 43's watch, he signed an Executive Order which provided the RIGHT, not OBLIGATION, to all US military personnel, whether active, retired, Reserves, Guard, or simply former military personnel, to salute the US flag or render a salute during playing of the National Anthem: whether indoors or outdoors, covered or not covered, in uniform or in civilian clothes. The order was intended to clear up any confusion and to spell out all possible scenarios. However, under previous directives or even generations-old, military traditions, this Marine should be saluting. That said, he may simply be performing this "hand-over-heart gesture" to emphasize to the crowd the proper manner in which we all should honor our National Flag during the playing or singing of our National Anthem. My take.

If he is wearing his cover he should salute.
From US Navy Regulations Section 1205
"Whenever the National Anthem is played, all naval service personnel not in formation shall stand at attention and face the national ensign. .... When covered, they shall come to the salute at the first note of the anthem, and shall remain at the salute until the last note of the anthem."

So the actual question is should he have been covered?