I think the thing that pains me most, looking back on it now, is that there was so much potential in the initial premise that went unrealized, and there's just no going back to it now. Just this idea of humanity as newcomers in the galactic community, trying to prove their worth and establish a place for themselves, and your character being the first human Spectre - having to balance the extraordinary privileges of the position with the responsibility of representing Humanity in a positive light, dealing with the prejudices of humans and non-humans alike (I would've loved to have seen some different reactions to Shepard's liaisons with aliens - imagine a human politico or military figure accusing Shep of pro-Asari bias because he's publicly involved with Liara, for example)...
I'd've also liked to see a bigger focus on investigative stuff as the series moved forward. Some scenario where you're working as a Spectre, dealing with various problems, and it gradually becomes clear over time that there's a guiding intelligence behind these seemingly unrelated incidents, eventually leading back to the Reapers. Wouldn't've been too hard to justify him/her putting together a "Dirty Dozen"-type squad a la ME 2 as a Spectre, either. I'd've preferred something like that to the whole Cerberus thing we eventually got, I think.
At the end of ME1, I could've imagined the series going more in that direction, and I'd've been thrilled if it had. I enjoyed what we did get - the characters and setting carried the series for me - but I feel the overarching plot shifted focus partway in, and a lot of those interesting elements ended up getting short shrift. It's kind of a shame, really.