I suppose the investigators would look for inconsistencies in 'the story' as told by different parties. If 'the story' is true then additional detail will be forthcoming and generally non-contradictory between accounts. If its all a cover-up then individual suspects will invent different details and give themselves away. 'We know at least one of you is lying.' At which point someone will betray the conspiracy for favourable terms, and the police will have a real witness. Maybe also this is the reason for a 'captain's log' - if that went missing too then there'd be even more suspicion.

True, but the lesser the number of crew members, the more chances that they'd have a consistent story.

But good point about the 'captain's log' though.

It is very infrequent that the whole crew is a part of mutiny. Captain usually has at least a few adherents as well. Kind of hard to explain away disappearance of the captain and his clique.

How is this different from a crime committed anywhere else? If my friends and I push another friend off a balcony, we could say he tripped.

Yes, but the scene of crime in this case is still available for the police to look at, and the dead body doesn't go anywhere.

The position of the body can in most cases show if the victim tripped or was pushed. Tampering with the body after the fall leaves even more clues for the police to find.

Tampering with the body - unless it is really, really obvious that he's dead, somebody is going to check the body and most likely even try first aid.

I suggest reading R v. Dudley and Stephens. http://en.wikipedia.org/wiki/R_v_Dudley_and_Stephens

Divide and conquer? Get them into separate rooms, say that one sold them out and then see if they turn on each other or something to that effect.

There is a strong dividing line between officers and crew on a ship. There is no reasonable way for the crew to recruit the officers to go along with eliminating the captain. In a mutiny, all of the officers would be killed, making any story the crew tells statistically improbable.

Is it illegal if it's in international waters and the crew doesn't take posession of the boat (theft)?

I think the law of the mother country applies on the boat. i.e. a boat flying an english flag is subject to english law on the boat. If you have your own boat, fly a pirate flag instead (i.e. not a member of any country), then you can make your own rules. However other countries might sink you.