Well the problems are more or less all over the trilogy. Let´s start with ME 2 where we gather 12 special hardcore killerdudes, -gals and pick up a robot on the way to assault the Collector homeworld before we find out that it´s actually a base we can actually blow apart.
Then let´s move over to ME 3 where the admirals responsible for defending Earth ask you how to defend Earth and Shep goes Hollywood inspiring speech time. After being held there for 6 months, they ask the guy who was in the council tower while the fleet was shooting Sovereign.
There is some stuff like the dreadnought who is actually unable to enter an atmosphere getting shot down or the plotshields of the Normandy in full force for the first time with the Reaper shooting down the two shuttles just in front of you while completely ignoring the tasty frigate. Is that too nitpicky? Hm, probably. 
Then we move to the plot where every time you hear Cerberus, you know the logic goes and takes a long and deep nap. From Hollywood superhacking, downloading data and deleting it from a device that actually works completely different twice, Shepard patiently waiting for the robot to call home, to Shepard doing Hollywood mook markmanship by closely missing the enemy with his pistol, besides having a 1000 different options, to fighting Cerberus troops with swords who think they are ninja. And throw in some nazi in the mix, by getting their own concentration camp with a soap machine.
I think there are also some glaring plotholes in the whole Thessia arc but well that´s the part where I get away from the computer to make myself some coffee and go outside for a smoke until all this autodialogue is done.
Edit: totally forgot this massive plothole of where did Cerberus get all these ships. I get the soldiers if I don´t look to closely and the equipment if we assume that fabricating smaller stuff is rather easy in the 22nd century. But Shep was assaulting the collector base six months ago with a measly frigate and now Cerberus has friggin dreadnoughts and cruiser fleets?
We also have awesome visuals in the space battles where Bioware ignored more or less everything they wrote about space battles in their codex besides being not really good tactics but the cinematics look cool and Shepard can yell Fire like in Zulu. I waited for the "wait until you see the white in their eyes."
I mean Reapers have eyes.
Isn´t that pure Hollywood, style over substance? And yes that stuff is substance. They pretend to write military scifi after all.
Then the whole mess of Mission Earth, I heard some people found the beam run immersive, some people think Anderson is the biggest idiot who ever yelled a command but well Mikefest is here, he can elaborate if he wants to. Myself I thought, I feel like a pyjak on Tuchanka.
And then we entered the exalted presence of the Catalyst who told us in his first few sentences "I am the Catalyst, the Citadel is my home," which turned the whole plot of ME 1 into nonsense...at the same very place where Sovereign was hugging the tower to open the relay three years ago. I mean, really, they just opened this big question about one third of the trilogy and not even one sentence about it even in the EC? About the rest, see above.
Sorry that I am not blown away by Hudson´s matrix architect ripoff. 
It seems to me that ME 3 was more similar to hollywood media than the previous parts and sacrificed quite a lot for drama.