Audio problem: When Kirk says, "Stop energizers," watch his lips closely - he really says, "Stop engines." Mike Okuda points this out in the text commentary on the Director's Edition DVD. The reason the line (and also the one following it) was redubbed was because someone pointed out during post-production that the engines couldn't simply be stopped on a dime. (00:39:08)
Audio problem: When Kirk makes his "old wounds" remark to McCoy, just before he steps out of the turbolift, we can hear the sound used to indicate the turbolift is moving, but the door is already open.
Audio problem: On Ceti Alpha V after Chekov urges Captain Terell, "We need to get out of here," we hear Terrell respond with "But the tricorder..." But his lips actually say "But the child..." The line referred to a deleted scene so it was recorded over in post.
Chosen answer: I imagine there was a memorial service for everyone killed. Starfleet's policy on corpses is probably to return them to Starfleet HQ where their families can collect them for whatever services or ceremonies they want unless the crewman had left instructions specifying otherwise. There's no telling why Kirk sent Spock's body to Genesis. Based on Sarek's reactions in ST3 he almost certainly went against Spock's wishes, unless of course, Spock left no recorded instructions and Kirk did what he thought would please Spock based on his being highest ranking officer and Spock's closest friend. It also seems very out of character for Spock to just assume that whoever he transferred his katra to would be able to handle it and carry out his wishes (McCoy certainly couldn't!). Ultimately it seems we have to chalk it up to a plot device to base the sequel on.
Grumpy Scot
According to the novelization, Kirk's intentions were to send Spock's remains into the Genesis sun. Lieutenant Saavik altered the trajectory of the torpedo beforehand, due to Spock's desire to see the Genesis effect for himself. The torpedo casing was expected to incinerate when entering the atmosphere. As pointed out by David Marcus in STIII when the pod was detected on the scanners, the gravitational fields were in flux at the time, and the pod had obviously soft-landed on the surface.