First of all, these improvements should be split into single player and multiplayer categories. Also, this switch needs to be incorporated:
--emulate=[PC/3DO]
This switch would be a quick way to set the options just like a certain version - PC (MOD music, no speech, perhaps some other changes to make it more like the PC version) or 3DO (OGG music, speech). The rest of the switches would add to and/or override that switch. At the very least, this will quiet down all of the don't-change-a-thing advocates. Every other change to the game should be disabled by default but accessable through the commandline switches and, eventually, a config file (and an editor for it).
On to my suggestions:
In single player:
Hyperspace time compression, as mentioned, is important.
A twist on the journal idea: Have stars that were specified in conversations blink on the starmap, perhaps with some floating text to let you know their significance.
A conversation backlog, IRC style, would be nice.
In multiplayer:
Network play over TCP/IP, complete with a tournament mode, fraglimits, timelimits, and chat. If more than 2-player combat turns out to be feasible - Team Deathmatch and CTF. Hey, if it works in THPS, why not Star Control?

Smooth turning radius - optional, of course, as the lack of this provides a good defense mechanism. In network play, the server should obviously have control over this.
Extreme tweakability - Scorched Earth style. Gravity should be modifiable, for instance. Simple tweaking of ships - recharge rate (in all of its forms), crew complement, speed and maneuverability - should also be possible. All of these should be modifiable in-game, especially when creating a server.
Handicap system - if a newbie is playing against a veteran, the veteran should have less crew, energy, speed and maneuverability (or only part of those, selectable before the match) than the newbie. This can be done by boosting the newbie's stats, lowering the veteran's, or both.
Those are my ideas for now. It would be nice to see some of those make it in after the stable release.