To be very specific about my gripes, I never liked that they transitioned from exploration and discovery to gun shooting in the two sequels. In Mass Effect 1 I felt like having guns was more about personal security and then the evolution of Shepard's story. There were conflicts that didn't require you to shoot anything and when you did it was more for self preservation than anything else. It felt more like an RPG in this way. Aside from the main story, there was very little weight attached to you using your gun. The gun shooting missions were mainly taking out teams of bandits or thieves that wouldn't change the story largely if you did or didn't take them out.
Starting with 2, there is no conflict in the game that you don't resolve with shooting at it.This immediately makes the RPG aspects useless as the talking only serves to set up the shooting, instead of being a possible resolution to whatever conflict you find yourself in. It was Gears of War with talking bits. Also with 2 Shepard became more than just a Spectre doing their job - s/he became "savior of the universe" which meant anything s/he did had huge weight to it. Now the objective was to go in guns blazing, instead of to explore and unravel. In Mass Effect 2 the only characters you really talk with are your teammates. Everyone else is just target practice.
Now, as far as combat Mass Effect 1 had huge issues (the controls were a mess, there were I think 4 or 5 different base styles the entire game, the inventory management sucked, especially when it filled up, there really wasn't any major difference between your team members and abilities) but there were things it did that neither of the other 2 games accomplished. Specific example - I once went to a snow world (can't remember the name) with a Geth installation and as an Infiltrator I was able to set up on a mountain about a kilometer away and snipe to my hearts content. There was versatility, distance, and control. In 2 and 3, all the fights are set pieces in which you MUST address the fight in THIS specific way. It always felt silly being an infiltrator and "sniping" a character 30 feet away.
People talk about the improvements with the Mako and the vehicles in ME2, but I disagree. The Mako had one major advantage in that you had to use it to beat the game. Not only are the vehicles in ME2 not mandatory to complete the game but they're behind a paywall as well. Another example about how all of the versatility of ME1 was stripped away.
Someone earlier in the thread mentioned how the Witcher has taken Bioware's RPG crown. I agree, because CD Project realizes that a great game lies in versatility and change to approach, not every one of Geralt's missions in the Witcher requires him to kill a monster. Meanwhile Bioware started ME in this way then distilled the series into 'talk to teammate, go on mission, token words, gunshoot' and away from the exploration and discovery. I hope that ME:A takes this into account.