The characters in ME1 were all paper thin. Yes, even Wrex. ME2's characters have much more development.
ME1 had an absolutely awful inventory system that was a pain in the ass to manage. ME2 got rid of it and made switching ammo types much easier.
ME1 had many terrible vehicle segments. They are gone in ME2. Scanning planets sucks, but isn't as bad.
ME1 probably has the least diverse level design of any game in recent memory. There are literally 3 layouts that get used over and over for planetary installations. Although ME2 suffers a bit from the "oh look, a pile of cover" problem, the more diverse layouts more than make up for it.
Weapons are more balanced in ME2, and ammo limitations actually force you to try different weapons rather than always relying on assault rifle or pistol. Special weapons were also a nice addition.
Combat is smoother all around in ME2, and squad members are easier to manage.
There are more city locations giving you a broader view of different types of civilization in the galaxy (I really don't know why people feel like ME1 had broader scope).
Larger number of enemy types in ME2. Still not great, but better than ME1.