Going forward, what are the biggest mysteries in the ME universe unsolved

The real reason why Addison left behind a "perfectly adequate career." She doesn't seem like the one to take risks, so why Andromeda? She also leaves Ryder with a cryptic response depending on the dialogue option you choose on Eos stating that she knows what she came here to do. Is she the unsung hero of the Initiative? There's the mystery around her trying to find Jien Garson in Uprising and getting hurt. Really think she got blown up/caught in an explosion when Sloane found her. At first, I suspected she might be connected to Cerberus/Horizon, but she isn't a xenophobe. I know she is connected to David Anderson, and so is Sloane...Sloaneykins is also connected with Commander Shepard if your Shepard served in the Skyllian Blitz.

Keri T'Vessa, her family, and why she got disowned. Typically, when parents disown their children, it's for a reason other than "she was taking pictures." What sort of pictures was she taking? Begs the question about who her family was and how connected they might have been to other more nefarious projects. She also seems to be about Liara's age, and as a high society girl, she would have been in Liara's same circles. Is she connected to Benezia, Aethyta, or.....Aria? I still think it's suspicious that she doesn't care about things like Kett attacks or the prospect of being Exiled. I'm also curious about whether she was awake for the Uprising; her dialogue seems to implicate no in some areas, but yes in others. I've been half tempted to ask the writers about this.

Reyes' connection to the Nexus. He mentions that he travels to and from the Nexus, largely using an alias. Except for body and ID scans on the Nexus would reveal his identity if his information was still accurate in the station's manifest. If he is able to get on and off the Nexus without anyone caring, I would think that he has connections to the dockmaster, Tann's office, and Kandros' office that are on his side. It's also a little suspect that he is so well supplied.

Leusinia/Paarchero: There's some serious side-eye if you choose Sarissa as your Pathfinder, plus some shadiness over Matriarch Ishara's death. There's also some curious tension between Captain Atanda and Sarissa. In choosing Vederia, she seems to display a level of ignorance that suggests that whatever drama the other two are involved in, she's been left out of. On the subject of Ark Paarchero, there seems to be hintings at left over Milky Way drama, and if you choose Hayjer as your Pathfinder, Tann seems awfully pleased.

Sergeant Talini: She figures prominently in Uprising. Where is she on the Nexus? I loved her character.

Yep, which is why I said "office." It would be a huge undertaking. With that said, the Nexus has core controls locked down to specific persons and specific departments. There was mention of hacked records was when Addison's credentials were used to modify them; meaning, to do so, it had to come from her level. I would think after the Falarn incident, Addison, Kandros, and Kesh would all be scrutinizing those records. Addison and Kesh are doubtful to do it themselves: Kesh is too busy, Addison can't be bothered. I can see Kandros doing it himself, or putting someone on it that he's vetted. Tann likes to have his fingers in everything, so I can see him taking an interest.

Either way, it would require all three of them to be looking the other way, or trusting the wrong person. Spender comes to mind as someone who would be involved with something like that. He effed over Addison and Sloane that way. However, he would have to had help otherwise Reyes' smuggling trips would have stopped with: "Hey, don't I know you?"

I think Addison's vague background and Reyes' lack of transparency are supposed to be  theory fuel for who conspired with the Benefactor/ who killed jien Garsen.

The Benefactors provide the only real plot point I want to see expanded upon or resolved from Andromeda.

Someone knew about the Reapers, and there was a lot more to the Initiative than really meets the eye, I think.

darkspace. The reapers use the Citadel relay to start the harvest. Obviously there is a relay in darkspace for them to get to the Citadel relay.  So what else is out there? Is there a giant space station the reapers hook up to before going into sleep mode? Or do they just hang around the relay for the whole time until its time to harvest?

There is an ingame reason for this, I can't remember what it is though. I think its on the wiki.