Mass Effect actually has pretty poor writing. In the first game in the first half Shepard doesn't seem to be aware of basic facts about Turian's, Asari and Solarians or the wider galaxy (and no, good writers don't need to make the player an idiot to info dump all this. Check out KOTOR2 for an example of how you do this write *hint, have the player tell someone else, instead of some loser instructing a Spectre badass on how guns work). And the appearance of Sir-Dying-In-The-Next-Scene and all his 'gee whizz I'm such a new happy recruit, I sure hope I don't get killed off in the frist mission' dialogue was particularly stupid when compared with his run-at-the-enemy-without-taking-cover-or-shooting death scene.
Also the entire starting conceit relies on Shepard blinding believing the words of a drunk smuggler hidden directly behind the corpse of someone who was shot in the back, with no other evidence. Plus 'you've got to believe my visions, I recently had severe head trauma so I can't be imaging it' isn't great motivation. Most of the initial motivation of the game involves the characters being hot-headed idiots who call people stupid bureaucrat for saying things like 'we won't arrest a man based on your word, when even you admit you didn't see him do it or even see him within 10 lightyears of the crime scene' and the other party members being stupid enough to follow someone with this motivation.
Naturally ME3 is really flawed, introducing a Deus Ex machina in the first 5 minutes and never strengthening it. Cutscene immortality and the ending etc
And ME2 doesn't fit with the idea of Cerberus of ME1 or ME3, dedicates the entire middle third of the series to an almost entirely irrelevant threat and makes it's own plot a sidequest in comparison to the sidequests.
That's not to say the Mass Effect series is bad, in fact it's brilliant. The characters individually are really well written, like seriously well written. The universe is established well, the gameplay is good and the game-story combinations are good with inspired things like the suicide mission. The level design in ME1 is divine. But the specific plotty writing is shoddy throughout the series