Usually I'm more interested what happens to everyone in a whole. But on that specific topic, as many have said before I would want more dynamic in terms of dialog options and general interactions. Meaning that it's not just some cut scenes set in stone when the protagonist gets all flirty with the LI. (Or couple like if it's already established) That goes for the actions as well it's very rare that the protagonist or the LI shows any kind of affection, it's usually just the normal dialog and at some key scenes they say something but often very very minimal. For example if Liara was the LI and the Shepherd and her gotten close before Thessia then Shepherd should have treated her differently, but it's the same thing as if the two were just friends, just seems weird.
This also extends to the way the two are in missions, the love interest should be a little more worried if **** hits the fan and vice versa. In short dialog and interactions should be different and more intimate between protagonist and LI on a regular basis. (Might be little things like being in the cabin or whatever more often or another greeting when all the dialog options are exhausted for this session)
I get the whole the night before the final push thing, and in Liara's case in ME1 that kinda made some sense (although bit shacky still) but Ashley or Kaiden? I don't think so. Which is also the last point which also many already pointed out, give them some activities to do, could be incredibly simple things drinks, a game of some sorts depending on what you choose and how much you actually have to do, the LI could reveal some personal things just to make it seem more real. Not things which affect performance or anything like that, but something trivial which would otherwise not be revealed.
Now I know some of those things are work intensive and satisfy only a narrow audience (in mass effects case might not be so narrow but still). Recording extra dialog for missions, briefings or many mid game conversations for each LI is probably a lot of work and only adds so much more to the immense voice recordings mass effect already has. Also takes time to set up animations for each love interest so they interact differently so I know that's much to ask.
But some of the things should be easy to implement with little effort. Like different generic greetings from the LI, just to remind you. Or those tiny dating bits. Or different interactions and dialog for the main plot points (like when the LI feels shitty). Those things go a long way to make it seem a lot more real and more immersive. (The extended cut in ME3 gave a special goodbye for the love interest, that's needed more frequently)
But for gods sake if the devs are gonna do all that by shaving off the PC optimization and it runs like crap then I'm not happy, and I'm not sure that would be a good trade. Although for some that would be debatable.
As for LI species, it's sort of difficult if you're gonna make it more immersive then you have issues with the size of the dating pool. I know the devs are keen on giving everybody a slice of the pie but that means so much needs to be available. 2 male one gay one straight, 2 female one gay one straight, and if I know anything about the mass effect community then it's one male female for each species and that racks up quite a lot of extra dialog and many many characters which is a problem and if you apply the gay options for every Alien species then it's even worse, it could be shaved off by making everyone bisexual but that seems unreasonable.
My most important wish is that you don't cut out the Asari LI, I know many don't think they're a priority (and I don't know why) but I quite like them (if people just didn't like Liara they could just make one more badass or rough like the cops on illium) and would suck to loose that just because all are into the Quarian hips.
But in the end it doesn't even really matter since I have little faith that one of devs actually reads this and even less that they take it seriously. But oh well one can dream.