There is definitely a lot of references to the past games, and many of them you might not even be aware of, not having played the previous games (for example, Tali's "emergency induction port" joke wouldn't make much sense, if you haven't talked to her about Quarian physiology in the first two games). It wouldn't be a good game design if this game was aimed at fresh players, but it is not the case.
Again, you definitely can play ME3 without having played previous games, and the core events and such will be explained to you - but you will still miss a lot; even if you have read the story summary of the previous two games, dialogues won't make nearly as much impact on you as if you had played them instead.
I disagree; I think the story and the dialogue were the weakest in ME1, and ME2/ME3 were on the same (higher) level in this regard, in my opinion. ME1 was more like an introduction to the series, it set up the lore, key characters, the story - but as a game in itself, it felt strongly inferior to me than the other two games.