Firstly, the choices you make and do they matter.
I was watching xcalizorz's Mass Effect 3 let's play on YouTube and noticed he made the same remark as I about how Mordin probably would've made the genophage cure regardless if you saved the data in Mass Effect 2 or not. And indeed he does. However, the female Krogan won't survive without the data, and thus Wrex (or Wreav if Wrex died on Virmire) is left to rule the Krogan alone, giving them and the galaxy a less positive future.
That and many more consequences of your actions don't become apparent if you play through the game only once. And even with multiple completions, you obviously need to have made different choices over the trilogy. There are also some very minor things, like Mordin won't sing his song as his last words if you didn't talk to him
I believe the Mass Effect trilogy is serious case of the journey mattering more than the destination. Because in the end, all your choices, like saving the rachni queen, authorizing the giving of a gun to the traumatized asari in the hospital, and not keeping Keiji's graybox, they all become one single number, the Effective Military Strength, that decides which endings are available to you, how much will the galaxy suffer from the red/green/blue explosion, will anyone step out of the crashed Normandy, and will Shepard take a breath if you choose the Destroy ending.
Destroying or saving the collector base in ME2 actually affects will you get the Destroy or Control ending, but only if your EMS is very low. Otherwise it won't matter; you get them both. It's the press A, B, or C to choose your ending. A thing that was not s'posed to be there. And many choices you make will give the same increase to the EMS regardless what you choose. Just under a different name in your war assets list.
I think that instead of this one value deciding everything, they should've made the ending sequence more like the attack to the collector base where to some degree you get to see your choices mattering. Like if you didn't buy the shield upgrade, the collector ship's shot kills one of your squad mates.
It would've been cool, for instance, if you saved the queen, to have the rachni at some point attack the reaper forces and clear the way for Shepard. And without them you'd have had to make your own way. Things like that would've been so amazing.
Another thing during my playthroughs that caused me to grow a certain dislike towards the series is how much there is dialogue and cutscenes. When I've already seen it all previously, I'd prefer to jump right into the action. It really harms the replayability. The multiplayer in ME3 is really good for that reason; no dialogue options to choose to get to shoot things.
I took time how long it takes before you get the control of your character at the start of Mass Effect 3 because it really felt like a long time. Almost eight (8) minutes! And the whole tutorial intro sequence before finding yourself on Mars takes 25 minutes in total. Going through that multiple times is painful. And the history-class scenery walk on Palaven's moon is also thing I'd have liked to skip.
A third thing -- maybe very minor for some, but immersion breaking for me -- are the M-8 Avenger (or alternatively M-3 Predator) cutscenes. Shepard will nearly always pull out the M-8 Avenger assault rifle for cutscenes even if you have a different one equipped or no assault rifle at all. I would very much like to know why this is. Because it doesn't happen in every cutscene; there are times when Shepard will happily take shots with the current weapon.
It happens in Mass Effect 2 as well, but mostly in the third game. Although in the second game it can be very noticeable when your Shepard doesn't even have assault rifle training. But what causes it? Because the cutscenes are made in the in-game engine and I don't understand why can't Shepard (and her squad mates) just use whatever weapons they have. Did the developers specifically put the Avenger in there every single time? I think I personally would have had hard time releasing the game with such an inconsistency.
And two final, somewhat related things...
In Mass Effect 2, the squad mates on Normandy will use the outfit you've set for them. But in Mass Effect 3 they go back to the first game's style of always using their default one. Is this only because they wanted James to be in his t-shirt? I think everyone else has their armor equipped while on the ship.
And why in Mass Effect 2 Shepard and her squad mates always wear their helmets (outside Normandy), when in Mass Effect they did so only when in an inhospitable environment. I think many use one of the visor headpieces for Shepard for that very reason. Although then Shepard will equip the default N7 helmet when the need rises... Good grief.
Miranda and Jacob also seem to only require face masks, which certainly is odd. I guess helmets would've looked silly with their "armors". At least in Mass Effect 3 there's an option again to make helmets invisible during dialogue. Thanks for that.
And, oh yeah; what the hell they did to peopl's eyeballs in ME3? Eyes seem to roam completely free from the head's movement, making characters do some seriously silly faces at times.
But I think that's enough about Mass Effect.