-Why did the reapers forget about the citadel until TIM told them it was important for something? In ME1, it's explained that the first thing the reapers do is take over the citadel, which is always the center of galactic politics. This throws the galaxy in to disarray and minimizes resistance. They also shut off the mass relays for everyone except them. In ME3 they don't bother disabling the mass relays and only take the citadel after TIM tells them it's a good idea.
-Everything having to do with the kid: who is he? Why is he there? Why does he take the form of that kid? What was up with the dream sequences? Who built/programmed him? Who built/programmed the reapers? Why? How is building a race of super-AI robots that kill all advanced organic life a good solution to stopping organic and synthetic life from fighting? How does killing advanced organic life and turning them into robot prawn preserve their essence for all eternity? Why does Shepard getting to the kid mean his solution won't work anymore? Why does he gladly explain to Shepard how to kill the reapers and undo everything he's apparently been working to preserve for millions of years?
-Cerberus. In ME1 they're a rogue military faction that kill wantonly kill people to keep their existance secret. They experiment with husks and rachni. In ME2 they're a covert organization striving to keep humanity safe. They have a few small operations overseen by TIM and while they have considerable resources, building the Normandy SR2 and reviving Shepard is said to nearly bankrupt them. In ME3 they're a powerful military force capable of, among other things, taking over multiple Alliance bases without effort, invading a top-secret research base on the Salarian homeworld, taking over the citadel, and fielding a fleet of ships against the combined Alliance forces. How and why do they change so much between games?
-Why is the Normandy fleeing a beam of energy at the end of the game? The Normandy was supposed to be fighting in the battle, right? Did Joker just pussy out and leave after Shepard got on the citadel? And I had EDI and Liara with in the final mission. Did they just catch a shuttle back to the Normandy while I was dealing with TIM and the kid? It took hundreds of soldiers to take the battlefield, so I doubt getting out would be very easy. Especially with two full-sized reapers there at the end. Who was aboard the Normandy as it was fleeing the magic plot device light? How did Joker not break any bones in the crash? So many questions.
-In ME2, blowing up a mass relay destroys an entire star system. In ME3, every mass relay is blown up. Am I to assume every star system housing a mass relay was destroyed, or did this magical colored plot device light not have that effect? We don't know, because there's no epilogue at all.
-For that matter, what happened to everyone aboard the citadel when the reapers took it? Did they evacuate, or were they just all killed? What was with the bodies on the citadel at the end, and why did it suddenly look so different?
-What happened to the fleets orbiting Earth? Did those aliens die when the Crusible fired, or are they just left orbiting Earth unable to get home because the mass relays were blown up? Or maybe they all died because the solar system was blown up by an exploding mass relay.
-What happened to indoctrination? In ME1, that's said to be one of the main ways the reapers counteract resistance. I kept expecting one of the major NPCs, maybe admiral Hackett, to secretly have been indoctrinated or something. Instead only Cerberus is said to be indoctrinated, and there are a few other references to it elsewhere. You'd think some indoctrinated personel working inside Shepard's combined fleets would have given the reapers an advantage. For that matter, indoctrinating anyone other than Cerberus, who everyone knows is evil at this point, would have been an advantage. In ME2, exposure to any reaper tech eventually results in indoctrination. In ME3, you pass out reaper tech to anyone who asks for it. I mean, one indoctrinated scientist with a bomb could have set the crucible project back months or even years, probably resulting in defeat for Shepard. It's not like it would have been hard for the reapers to figure out what Shepard and co were up to. For that matter...
-Why are the reapers so bad at their job? They're supposed to be crushing resistance and harvesting organic life. But for whatever reason, they either don't find out about the crucible (even though everyone seems to know about it, and random scientists discuss plans for it in public), or they don't care. Again, one reaper could indoctrinate some scientists, find out where it was being built, and blow up the crucible and all the people working on it. Game over. Instead, the reapers appear content to attack planets one at a time and do nothing to disrupt resistance, giving Shepard plenty of time to gather support for the final push. With how sloppy their invasion is, it's amazing that they managed to win in any past cycles.
-In ME1 it's explained that the citadel is the center of the reaper invasion, and one of its purposes is as a giant mass relay to bring the reapers in from the dark space beyond the galaxy. That suggests they need a mass relay to get into the galaxy, otherwise why bother building the citadel that way? So why is it then so easy for the reapers to invade without using the citadel as a relay? They made it to the galaxy in under three years. So why bother with the citadel relay in the first place? Sovergn could have just sent them a message to come without doing anything it did in ME1, and nobody would have known about the reapers. What was the point of ME1, again?
-Why does the human reaper look nothing like the other reapers? We see the core of a reaper in ME2, and it's not some kind of giant skeleton. It's also never addressed how pulped human can even turn into a reaper. I mean, there's iron in the human body, but not very much.
-All the foreshadowing about humans being somehow special or neccisary for the reaper's plans is completely absent from ME3. There's no reference to genetic diversity, and the actions of the collectors are only references as "good times" between squadmates. There's no explanation for why the collectors were trying to build a human reaper when the entire reaper fleet was only a few months away from the galaxy anyway. In fact, there's practically no conversing with reapers even though the game is full of them.
-Since nobody seemed to believe Shepard about the reapers, why didn't Shepard just use the reaper corpse TIM found in ME2 to prove that, at the very least, they predate the Geth by millenia? I mean, sure, you're in a hurry, but just letting some scientists poke around the outside of the dead reaper for a week couldn't hurt.
-Why did the Protheans bury an artifact on Mars that contained plans for the crucible but apparently no information on the reapers? Or if it did contain information about the reapers, why didn't anyone find that information? Was the artifact just sitting around in a storage closet until Liara decided to look at it?
-Why is Admiral Hackett's plan to get an army and attack Earth? An attack is doomed to fail without the crucible anyway, and the crucible will supposedly destroy the reapers, so why not just build it and use it in place? Sure, it turns out that they need the citadel and the reapers move the citadel to Earth, but Hackett certainly doesn't know that's going to happen when he tells Shepard to put together a fleet for liberating Earth. Lucky thing the reapers decided to move the citadel there instead of hiding it somewhere. It is a mass relay, after all, so they could have just towed it to the middle of nowhere so the resistance forces couldn't find it.