[*]Rachni (Almost certainly not going to appear)

If there's any species that need to be rectoned back into the series, it's the Rachni IMO.
Aside from the un-matched advantage that Rachni can provide in settling new worlds (colonies in a few days), as well as relyable soldiers that can be easily replaced (queens birthing hundredes of eggs over several hours), the Rachni are the most alien species left in the setting after the end of the trilogy.
When it comes to truely different perspectives, none of the other species even comes close to what the space bugs offer. The Geth were close in ME 2, but they were "fixed" in ME 3 to be more like us. I want to see more than just humans in rubber suits, I want to see a universe that doesn't automatically conform to our moralities, or our way of thinking, and most importantly, I would like to see these things in something that is not imeditatly labled as a "bad guy" for our protagonist to kill.
Of course BioWare will give us new aliens to encounter in Andromeda, but how many of them are going to be alien to the same level as the Rachni, or Thorian, or ME 2 Geth? They don't exactly have the best track record when it comes to adding in new "alien" elements or characters to a franchise as it goes on.
Look at Dragon Age, in Origins you could deal with intelligent demons, werewolves, a talking sylvan, Awakened Darkspawn, ect. You could recruit a golem into your party, enlist the aid of savage wolf-men to help you, chat it up with the Architect, ect.
Flash forward to Inquisition and all of the demons you encounter are mindless monsters (outside of two dialogues with little more than a few lines), golems, werewolves, and Sylvans are nowhere to be seen, and the fantasy creatures that are present (like Giants) are just XP bags for the player to kill. Anything that is not imeditatly recognized as human or very human-like is automatically hostile and in need of slaying.
Mass Effect starts out strong with the Thorian, the Rachni , the Elcor, the Hanar and the Geth, but over the course of the trilogy these alien aliens are killed off, shoved off camera, made into joke races, or "corrected" to be more in line with our way of thinking. Any new aliens added to the universe were just more humans in rubber suites; the Leviathans where just Reapers: Skin Edition.
I would much rather have Bioware preserve what little alien elements that remain in the setting rather than hoping that they can buck their established trend and create something new and unique. (Again IMO)