I don't think scientific impossibilities are a bad thing at all. At the end of the day, this is science fiction. Of course it's going to have nonsensical elements that just can't work in real life. Realism would mean we play as a NASA bureaucrat who tries to get another drone deployed to Mars in 10 years or something. It's just not fun. Until we actually leave our planet and/or encounter aliens (which isn't likely in the foreseeable future), any science-fiction story relies on convenient nonsense by defintion.
That said, I do think there's a difference between scientific mumbo-jumbo that was introduced early in the setting and makes some amount of sense when presented to a layman (the titular Mass Effect, for instance) and something that is just so mind-boggingly ridiculous that thinking about it for a minute makes the entire concept fall apart even with no proper scientific knowledge (such as the Synthesis beam). The first preserves the suspension of disbelief. The latter does not.
In a universe with magic, this means that a mage throwing a fireball is OK if it was explained it's a common magic power, but introducing a character that can make the entire planet love each other with a snap of their finger with no explanantion is just cheap. Neither is more realistic than the other, yet the audience can learn to accept the fireballs, but probably not the wave of instant peace and love.
So yeah, I disagree with In Exile that it's all just space magic nonsense with no distinction. Building a credible world, or at least a world with a convincing enough veneer of credibility, is important to writing science-fiction that I enjoy. For all its faults (Project Lazarus, urgh) and missed details, I thought Mass Effect did a good enough job of that until the ending made the entire thing crash down.
And yeah, I'd like to have an explanation on how they managed to get to Andromeda with no need to discharge their drive core. If what Mac Walters let slip by in a recent interview is real, the journey took 600 years. That's actually somewhat consistent with the speed of FTL as described in the original trilogy. But where did they discharge their cores, is a question that kinda needs answering IMO. It's a rule of the setting. Ignoring it now isn't a great idea, no more than it would make sense for all the mages in Dragon Ages to all be able to turn into dragons at will with no explanation given despite the fact that magic, by its very nature, is nonsensical.