I would like to see a few additions to the game myself, some have been mentiond already but im going to post them here anyway.
First, a menu option or pregame lobby that will alow me to get my friends in a group instead of having to hope there is room in a match after i join. It gets a little annoying when you keep connecting to the same match that doesnt have room for me + 1 or 2 friends.
Also, i havent found a way to customize a game type so that it excludes bots. It would be great to have the option to play only aginst real players.
Abilities could be handled a little differently. For a game that is based on team work it seems kind of odd to limit players to 1 or 2 classes per character. If you put points into the general tree (which almost seems mandatory for atleast 3 abilities) it really only leaves you with enough points to make 2 classes competitive at lvl 20. Yes I understand that you have all the core skills needed for a class but if your prefered classes are medic and engineer who really wants to play a solider or operative that only has 1-2 abilities (if that). I see alot of matches where the objectives arent getting done and im on a character that doesnt have points into the class that needs to do the objective. My only suggestion would be to allow a certain number of points to be spent in each rank instead of having a set amount of points for everything.
It would also be nice to have more matches with several objectives to increase match length, and more matches that have multiple objectives for all 3 classes ( medics excluded because they dont have interactive abilities like the other 3 classes ). This would also allow the maps to be opened up to their fullest for the entirety of the match rather than having everyone congregate around small sections of a map while one main objective is in progress. You could also create match types that arent completely offensive or defensive. For example you could add a match that requires both sides to retrieve an intel package and carry it to a specific location on their side of the map. Have doors and ramps that could be opend/close construced/destroyed to help your team or hinder the other team and add a count to the number of captures per match instead of a one time completion. (basicly just a Brink style capture the flag).
Last, (someone has already made a thread) operatives need love. Alot of matches dont have a need for operatives at all. Hack points are rare in the game and need to be added in even if they are only secondary objectives. Operatives could also use a buff The ability to cause enemies to show up on radar doesnt make up for their lack of a buff, it is a team based game afterall and buffs are a big part of it, not to mention the fact that lvling as an operative is way too slow because they dont have a buff. I read a comment about melee damage being too low considering how difficult it can be to actualy melee someone. Perhaps operatives could buff melee and slide damage a little, this would also make the light class more appealing to people that dont like the pistols and make disguise a little more fun

. As it stands right now operative seems more like a lone wolf class in a game that isnt very friendly to lone wolves, they dont really need buffed just fine tuned to make them more group friendly and to bring them up to par in terms of lvling speed for anyone who wants to lvl as an operative.
I have other minor suggestions but they have mostly been mentioned and these are the major things that i think would make the game better for alot of players that want to enjoy brink long term.