Well, some of what I'm about to say is going to probably just echo what has already been written.
1) Improving the crew management system from how it works in SHIII. Being able to assign watches and default battle stations would be nice. How about the ability to order drills which might improve crew efficiency for specific tasks? Though I don't think most players would forego that x1024 time compression going to their patrol area to drill.
1.5) Some sort of crew morale might be interesting, as they somewhat function as automatons in SHIII. For example, maybe your boat has been out on patrol for a long time, and your boys are feeling fatigued/depressed/whatever. Perhaps you can anchor your boat near an atoll and allow the crew a chance of recreational swimming/day at the beach, and morale improves. Of course, if an enemy patrol aircraft finds you under such circumstances, you could be seriously screwed. Crew members could also have a regard/popularity w/the rest of the crew or certain segments of the crew, and if they get killed/injured, there could be a weighted response on the rest of the crew dependent on that regard/popularity. Who knows, if a hated officer were killed, morale might even improve!!! You might also have to spend renown transferring out an unpopular crewmember to bring in one who "plays nice." Also, as a skipper, you could speak to crewmembers and try to improve morale, that way, though that's starting to be more of an RPG rather than a sim
2) I would like to be able to play the Japanese, and the ability to fly the Glen floatplane, etc., in certain missions. I know this will almost certainly fall out of the scope of a subsim, but I think it would be a nifty thing to be able to do. Other nationalities would be nice besides the U.S. The Dutch would pose some interesting challenges, for example.
3) the ability to give simple orders like "shadow ship A at current distance/bearing/whatever," etc., or "If event A happens, react w/plan B" Not necessary by a long shot, but I don't think it would be a bad move. I can tell you, trying to shadow a convoy in rough seas at 32x while waiting for night can be a bitch!!!! And an immediate crash dive at the first spotting of an aircraft would be really good w/out having to spend time using the interface. Well, unless you're in shallow water, in which case it might be a Bad Move.
I like the idea to be able explore more compartments of the ship, and if a crewmember is off watch he'll be in his bunk, seeing the number of torpedoes go down as they're used, etc. I don't think that's entirely necessary, however. Wouldn't it be funny to go into the head and find an issue of Stars & Stripes/Volkischer Beobachter to read?
Are there default tracks that can be played on the gramophone? I haven't explored that. My blazing the Grateful Dead or Jimi Hendrix is probably a tad anachronistic, and the Andrews Sisters or Duke Wellington might be more appropriate. Though I suppose it could be argued that Pink Floyd's "Echoes" might be even MORE appropriate!!!
I'll add more if I think of anything.