1. Why did the S.H.I.E.L.D. base collapse?
So, right at the start of The Avengers, Loki appears in a S.H.I.E.L.D. base via a portal generated by the Tesseract. After he steals the Tesseract, residual energy left by the portal implodes, sucking the entire base into a huge hole.
Yet, later on in the movie, when a much bigger portal was in the sky above New York (big enough to allow Chitauri Leviathans pass through it, in comparison to the one that was just about big enough to let Loki pass through), there was no residual energy to speak of after it was closed and thus no implosion. WHY?
2. How did Loki even survive the movie?
It was specifically stated by Thanos' servant and the Chitauri's leader The Other that, should he fail to enslave the Earth, Loki would be made to pay by the Mad Titan - indeed, he would be "made to wish for something as sweet as pain".
Three years on and Loki is still very much alive, lording over Asgard, and Thanos hasn't punished him at all. Granted, he might have plans and further use for him, but why include the scene about the torture he'd be exposed to if he failed if it was never going to happen? Maybe The Other was just being a dick.
3. Knocking someone out undoes the control of an Infinity Stone?
The Infinity Stones are powerful artefacts that were forged before the creation of the universe itself. There are six of them - each with planetary levels of power - and one of them was used by Loki to create mind-controlled flunkies to do his bidding. In this case, Hawkeye.
Apparently, however, simply hitting someone in the head with the force of a human female (admittedly an extremely tough and skilled human female) is enough to undo its effects. Pretty pathetic when you actually think about it.
4. Why was Loki's hologram using a computer?
The scene in which Phil Coulson meets his (temporary) demise sees him approaching Loki - while the villain is using a S.H.I.E.L.D. computer - wielding the gun forged from the Asgardian Destroyer armour.
Whilst Coulson is threatening Loki with the gun, the trickster appears behind him and stabs him through the heart with his staff. This has to make you wonder; why the hell was Loki's illusionary hologram using a computer? He didn't know Coulson was coming and Thor - who was right next to Loki inside the Hulk-proof cage - hadn't seen the "real" Loki disappear (evident from the fact that he didn't warn Coulson that Loki was about to trick him). Are we just meant to accept that holograms use computers??
5. How did Tony Stark guess Loki's location?
As soon as Tony Stark established Loki's plan - to make himself visible by giving himself a stage as he guided his alien army towards world domination - he instantly knew exactly where he would be; Stark Tower.
How the hell did he know that? It's not as if Stark Tower is the only tall building with lights at the top of it in New York, let alone the whole United States of America, let alone the whole God damned world. Loki could have been in Paris, Hong Kong, London or Rio de Janeiro (or anywhere else), but Stark conveniently guessed exactly where he was - and it happened to be the stupidest place he could have chosen.
6. Loki really couldn't figure out how to control Tony Stark?
Loki seemed to have done his research on the Avengers (he referred to Captain America as "the soldier" as soon as he first encountered him in Stuttgart and knew enough about the Hulk to want to unleash him as the main part of his plan).
And yet he tried to control Tony Stark, failed because of his arc reactor, and couldn't figure out what had gone wrong (the arc reactor is one of the most prominent and well-known factors of Tony Stark's existence, for Christ's sake). Surely he could have just placed the staff on a fleshy part of Tony Stark and had it do its mind-control thing straight after the initial failure. Then again, we have already established that he's a bit of a moron.