Ehem...
Now, I will try not to sound superior and condescending, but there are answers to every one of these issues. Some are, admittedly, not spelled out in the games themselves, but if you can take the liberty of questioning everything the characters in a fictional world do, then it's just as valid to take some time to figure out how they might actually make sense.
Machine Man 1992 said:
1: the existence of the Collectors contradicts the conflict of ME1; if there was a race of Reaper slaves hiding in a convenient mass relay that only they or there masters could go through (hence the IFF you plucked out of a dead Reaper), then why didn't Sovereign go to them instead of fucking around with Saren and the geth?
2: it's plot is barely there, consisting mostly of side missions that, as it turns out, have fuck all to do with anything. The characters, while well written dialogue wise, are basically a check list of cliches.
3: the plot relies on the main characters being idiots; at no point did any of them suggest bringing video or sensor evidence (or hell, a cadaver) to the galactic authorities to prove that Reapers and Collectors exist. And if that doesn't work, give Emily Wong a ring. Nobody ever thought of leaving a nuke like the one they left on Pragia onto the Collector ship to blow the thing to kingdom come.
4: Finally, the end shows that the didn't need the Citadel or the Collectors at, since in less than a year, they reach the galactic rim and begin their invasion in full. So what was the point?
1: The Collectors don't contradict anything. They may have been a resource Sovereign should have used, but in all of ME2 you only ever see one Collector ship. The one at the beginning is the same one you encounter twice more, and once you blow it up, the collectors don't send any more at you. Clearly, they weren't built to stage a full-scale assault on anything. They work on the fringes, with just one ship powerful enough to subdue a single undefended colony. Sovereign used the geth because they had thousands of ships at least on par with the Council races, and were willing to follow him. The geth made for a much stronger force than the Collectors, who were designed to be more of a black-ops organization.
2: I never grasped the school of thought that says everything in the plot must directly contribute to furthering the action. I completely disagree. This may be a simple debate about story structure and mechanics, but I don't see why you can't have an interlude in the main plot to tell a tangentially related side story, one which builds toward your final chapter by introducing tons of characters and a great deal of relevant information about the galaxy Shepard is saving. What's wrong with fleshing out your setting? Why does everything Shepard does have to be directly against the reapers? The options for this middle chapter were 1: Giving Shepard something to do while waiting for the reapers, or 2: Starting the galactic war one third of the way into the story, which would make less sense, since Shepard literally
just stopped the invasion. I think they did the best they could considering the limitations.
And if the characters being rather cliche bothers you, that's your preference. I don't see the problem. For the most part, they started with an archetypal character and built on that to create an actual person with dimensions.
3: This is a non-issue. The characters not doing what you think would be a smart thing to do does not make it badly written. If there had been a solution to these problems previously mentioned in the game, then it would be bad writing. But since there was not, we have to assume that they did what they could in that situation with the available information.
Where exactly were they going to get video evidence of the reapers? The Council already heard Saren and Benezia talking about them and dismissed that claim. There was no proof of their existence until Virmire, which was vaporized. The Council says that they went to Ilos, and the prothean VI defunct. There is no proof of the reapers beyond bringing one to the Citadel, and... Wait, they did exactly that. And the Council still denied it.
4: And finally, the point of the Citadel being a relay to dark space is that way, the reapers can start the war by exterminating the leaders of the galactic government and controlling the relay network. Yes, they can just travel to the edge of the galaxy and invade from the outside, but it is much more efficient to start with the center of galactic power. The reapers have been doing this for a billion years. They have refined it to consume the least amount of resources possible.