I think a lot of good points have been made by others already but I'll chime in with my two cents FWIW:
A New Normandy-If you biffed over the Illusive Man at end of ME2 by blowing up the Collector base as I did most of the time, it would be logical to conclude that Shep won't command the SR2. My idea-and of course it's just that-is that the Spectres are a more potent organization than generally known. Thus, they have the clout to build their own Normandy have have been developing it in secret since late in ME1. Of course, it will be bigger and badder than the SR2.
Space Combat-This worked as a nice departure in Halo Reach and would be equally fun in ME3. This should be a side quest or two, not the main modus operendi for the game.
A Hot Female Chief Engineer-This is all too rare in Sci-Fi in general and would simply make for a nice change of pace. I envision someone smart, funny, assertive (it's her ship and she allows others to use it on occasion), perhaps Irish as a nostalgic link to Stark Trek? Should Shepard have a shot at her? What do you think?
A Substantial Side Mission for Kasumi-Though I think Kasumi's DLC was OK, her character didn't get close to sufficient examination. I envision a side mission on Earth (pre-Reaper arrival) where she and Shep visit her family in Tokyo (the visuals for this would be worth it alone). Her family (parents in particular) are honorable and conservative which will make for some very interesting dinner talk given Kasumi's line of work.
. As it turns out, her family is at risk due to retaliation from one of Kasumi's past escapades so she and Shep have to deal with the threat... By the way, just as we all want to see what Tali looks like we also want to see what Kasumi looks like too.
A Visit To The Hanar Homeworld (Plus Hanar Squadmate?)-It would just be cool to get more insight into this fascinating race. If the logistics could be worked out (height on the Normandy), it would be hip for Shep to have a Hanar teammate. I envision armor, a compact-strap on back beam weapon, and one of the meanest melee attacks on the team (Hint: Their tentacles aren't just for standing...).
Teammates and Re-acquaintances: At minimum, Tali, Garrus, and Joker must return as Shep's de-facto road crew. Beyond the Hanar I previously suggested, EDI should return in hot corporeal form (either huminoid robtic or light contained within a mass effect field (something like Cortana from Halo). She'll be Joker's love interest and his greatest defender. Joker could be put in jeopardy during the game and we get to watch as EDI applies a major beat down on the threat.
Though optional, I think I'd like to see Kasumi back as a teammate where her pilfering skills can be put to good use (stealing Reaper tech perhaps?). Also optional-but probably not recommended-would be Liara only because one would think she would be more effective against the Reapers elsewhere (intentionally vague-Lair of the Shadow Broker DLC-highly recommend if you haven't played it). None of the other ME2 temmates should return as such in ME3. However, I think it would be nice to visit them for status and continuity purposes. These shouldn't be time consuming or even necessarily in person. As for new teammates beyond those previously mentioned, there are many options: A female Turian soldier, an Asari Spectre with integrity (no explanation by design), a Yahg (just kidding but a "domesticated" one would be pretty formidable though...
), or someone from a new species.
More Weapons and Armor Options: I'm sure there are plenty options I can't think of right now, but three are the return of grenades (with optional "warheads"), and a concussive rifle/pistol that fires Xplosive rounds that not only do damage but push the target back with each impact-effectively preventing the target from taking any retaliatory action. The third idea is a one-person mech (sized like the loader from Aliens 2) with crew-sized weapons and decent armor that Shep or other teammates can use when appropriate. It would be dropped and picked up by the Normandy at low altitude and speed.
More RPG, Less Shooting: Make no mistake, I enjoyed the shooting in ME1 and 2 and want more of the same in ME3, but I do think relationships and politics should play a greater role in ME3 than it did in ME2. I think the basic premise of ME3-rallying various races to fight the Reapers-will require this change in RPG/shoot balance. To the credit of ME1 and 2, both games required decision making that should make a RPG-bias easy to implement. For example, the amount of persuasion Shep will need with Rachni will differ greatly depending on how you handled the fate of their queen in ME1, not to mention your decision about the Geth heretics in ME2...
Regardless of what ME3 ultimately does or does not include, I'm really looking forward to it!