I agree with others that the grapple system really needs to be looked at. It seems very out of place because, as far as I can tell, nothing seems to factor into it really. Someone with no combat skill can grab even the most trained of fighters with relative ease. It has been very jarring to see one combatant winning a fight fairly easily, only to get grabbed and suddenly be helpless. I know this has been discussed in other threads, but I think part of the problem stems from the fact that grapple is sometimes used for RP and sometimes for combat. Thus grabbing people is fairly easy because you want to be able to stop someone leaving a room in a friendly manor. You also want to be able to drag someone who DCed somewhere safe, etc.
My main suggestion for this would be to split the current grapple into two separate systems. One would be 'grab' and be for RP purposes. No attacks could be made, and breaking it would be very easy. The other would be 'grapple', and work largely how the current system does, but hopefully with more use of skills and stats to determine how things work out, as well as a risk of being injured in the attempt so it isn't just a free attack.
Okay, enough about grapple.
For the Matrix... well, I'm sure everyone would really love it, but just as sure that it would be an absurd amount of work. Personally I'd be happy if the Grid was just... a bit more integrated into the world. Right now there is... well, virtually no reason to go there. I think 90% of people go there as nothing more than a mail service for their grid mail, and occasionally to skim the forums. Finding nodes is difficult, there is depressingly little information there, and even major corporations have virtually 0 Grid presence. SK doesn't advertise its cyberware. It'd be a great place to put in game information in about their products. There is this strange sort of addition with 'The Mind' as things on there are theoretically discoverable on the Grid, but good luck finding even the slightest trace of most of what is there. Combining the two a bit better and in a bit more IC format would be wonderful.
It would also be great if there was a reason to be on the Grid. Right now it is a bit of a catch-22. There aren't any people on the Grid, because there isn't much there, because there isn't any reason to put anything there, because there aren't any people on the Grid. I think putting more information there would be a good first step. Then again, if there really is plans to replace the whole thing, then I suppose there wouldn't be too much point to putting effort into it.
One thing I'd really love to see is more robots/drones. I know there are a couple of eyebots or whatever they're called floating around, but I think it'd be wonderful to see more of them, to see little drones running around performing small tasks, and particularly to give players access (or more access) to rigging of drones and what not. It might be that I just haven't encountered it ICly yet and it is really out there, but giving a player the ability to have some eyes in the sky floating around, or little mechanical assistants/bodyguards or whatever. I just feel like this is a rather classic element of cyberpunk that seems to be virtually non-existent in the game. As a short term thing, I think it'd be great to have a few more eyebots wandering the streets, keeping an eye on things, to give the presence of more technology and the feeling of being watched by big brother. It would also pave the way for seeing player controlled eye-bots and such and having less of a 'well, some other player is watching' instant mindset when they're seen in odd places.
I support the bodyguard suggestion. Give a 'bodyguard' command and any time someone does an attack on the person being guarded, there is a chance for it to target the bodyguard instead, or perhaps just enter combat with the bodyguard instead of the target entirely.
Disconnecting. Someone mentioned how strange it can be that people are always 'asleep' when they disconnect, even though they are actually theoretically potentially going about their job and such. I think it might be nice if there was a... well, a way to set that someone is disconnected, but going about their daily life instead of simply asleep. Perhaps let people set a space of time when they would be actually asleep, and a time when they would be doing their jobs or otherwise awake, and let them set a message that reflects the latter which it would automatically change to at the set time so long as they're in some particular area (like their own home). Maybe not take them out entirely, but adjust their message to something like “is off on their daily business right now.” and them logging on would be them coming home from shopping or working or grabbing a morning coffee. I realize there are significant difficulties with this, and it may not be feasible, especially as I've described it, but some way to not have sleeping bodies all over the places in our homes and such would be wonderful.
Permadeath – I'll throw my 2 chyen in on this. Personally, I don't see any problem with how the system is now. Increasing the penalties for dying would be a terrible decision, as it would only push people harder towards never taking risks. And honestly, I don't see the system being 'optional' as some put it as a flaw. Not all characters are risk takers. Not all characters want to be so extreme and live on the edge. It honestly feels like a slap in the face to suggest that playing a character who doesn't have a death wish is somehow not playing the game correctly. I'll leave it at that after spending half an hour typing, deleting, and retyping various responses.
Training – I think it would be nice to have some level of in game training. I don't think it should be much. I played a game recently that was all 'improve through skill use' and at times I found it very entertaining and loved it, but I also found myself grinding terribly, and realizing how hard it was for people that couldn't be on much to do anything, and how much less I was actually RPing. That said, I'd love to be able to get an extra UE a week or half a UE a day or whatever through some IC means of practice or training. Maybe visiting the gym for half an hour (in a way somewhat similar to how SHI works) gives you half a UE a day towards a physical stat. Or buying some sort of 'learn X language tapes' would slowly trickle in some points to speaking a language.
As I said, I think the amount should be very small and limited so as not to give people with more free time a large advantage, and I think the activity required should be relatively quick so people without a ton of time could do it without serious commitment. I suppose in some ways this amounts to a 'more UE please' request, and perhaps some additional restrictions could be placed on it. Maybe it's only valid for very low skill levels of things, giving people a means to gain a little passing familiarity in something as a sort of side hobby without having to devote overly much to it.
I suppose my thing is I'd love to see a bit more 'on screen' use of UE. I'm guilty of it too, spending my UE with little to no RP around it, and I'm going to try and avoid that more, but I really think it would be nice to have some sort of motivation, or even tools to aid in the RP like language books or tapes, computer/vehicle manuals, dojos, etc. It is though a fairly minor concern overall, as much of this can be obtained by the players themselves, but currently the only training I ever seem to see RPed at all is spars.
Gadgets – Thecraftydragon mentioned this, but I'd like to as well. I'd love to see more high tech gadgets in general. Right now there aren't (or at least I haven't seen) all that many things that make Sindome feel like it is set in the future beyond a few of the big things like cloning, the dome itself, and the chrome. I think the robots I mentioned above would help increase that feel, and perhaps changes would come about as a result of the introduction of the matrix, but even pieces of tech that we have now might be cool additions. Earpieces to talk on your phone without holding it for example. Glasses that can act as small TVs for the wearer. I'm bad at coming up with this sort of tech, but I imagine we could get plenty of suggestions for small things that could add to the immersion some. And yes, I know there are a fair number of things looking around in the city, but I'd love to see it more on an individual basis.
SIC chatter – Related to what bean_dip said, I'd love it if some scripts could be set up (though babble on maybe) to have some random chatter happen on SIC to make it seem a bit fuller. Wouldn't have to be overly complicated or anything. Maybe just a huge list of random names that throw out an occasional “Hello Withmore” or “Call me again” or “Sorry private SICer, no.” along with a few other things we commonly hear other players say, and random snatches of conversation. Doesn't even have to be a full conversation back and forth, just random snatches of it to represent the mundane stuff you normally ignore kind of slipping past your mental filters. Some people may not like the extra 'noise' it creates, but honestly that's supposed to be a downside of the chip, is that there is tons and tons of noise from it.
TL:DR Grapple needs work. Matrix please. Robots/drones please. Go bodyguarding. Sleeping when disconnected alternatives. Permadeath is fine. Training. Gadgets please. SIC chatter.
P.S. I'm sure everyone would love more chrome. This is cyberpunk after all! I think more exclusive cyber would be great, make you chose between getting option A or B like the limited slots in the eyes and ears do to some extent.