Though I'm hardly an expert, I've partaken in some discussions about comic-book "reality" with people who are more knowledgeable about what goes on in those colored panels than I am, so I'll pass along some of that info if it'll entertain you. But one important distinction: in the movies (and in the "Ultimate" Marvel comics continuity), the Avengers are formed under the direction of SHIELD, while in the main comics continuity (aka "616"), the founding members were established heroes that mutually decided they should work together and hang out at a clubhouse in NYC.
Rules of Engagement:In both cases, the Avengers end up having a pretty loose relationship with SHIELD--they're not a government taskforce, which frees them up to stop villainy that threatens all of Earth, both offworld and anywhere on the planet, without having to consult with a chain of command or political policy. They do have to answer for their actions, and that's usually where the ties to SHIELD come in, though most of it happens "offscreen." It's implied that they have the same legal help and considerations that are given to the Fantastic Four (who are also based in NYC). It's probably worth mentioning that both Avengers and the F4 have friendly ties to major corporations (Avengers have Stark Industries, the F4 have whoever Reed's working with--whoever owns the Baxter Building, I guess). But at least in the 616 continuity, they eventually mention "onscreen" that both the Avengers and F4 do have legal issues that need to be addressed, and in both cases they're largely handled by the Marvel Universe's best lawyer, who's had time with both teams...She-Hulk. She had a brief comic series recently where she went to work with a firm that handled "superhero" law cases, and you can check that out if you'd like to see some fun stories along those lines. Generally speaking though, it seems like very few lawsuits are filed against teams that are personally responsible for preventing the deaths of the people that would file those lawsuits.
Short version: the Avengers do what needs to be done to protect the Earth "in the moment", and let their hired professionals (SHIELD contacts, corporate lawyers) sort out any reparations they need to make after the world's been saved.
Anger Management:As mentioned above, NYC is host to the Avengers and F4, who have no shortage of foes looking to destroy their homes. And that doesn't even take into consideration the Hulk's rampages, the fact that Spidey patrols the city and has his own rogues' gallery wrecking the place to get to him, or the times that the X-Men pay a visit from upstate, or the latest demonic horrors attacking Dr. Strange's home (also in NYC). Consequently, there is in fact an organization--I think it's called "Damage Control", admittedly not very creative--that's mainly concerned with cleaning up and rebuilding all the wreckage from superhero fights. I believe they're mainly in NYC (they might be a part of Stark Industries), though they probably have branches in other places where such services are needed. I've read (on the internet, so take it with a grain of salt) that at the end of the movie, the news-ticker scrolling by during the montage of media reactions made reference to Damage Control beginning cleanup in the wake of the attacks. Oh, and I think in the comics there's probably some kind of superhero-hazard insurance, but it's one of those optional things that you have to decide if you're going to take, so if you don't take it you could be screwed if the Hulk comes crashing down onto your car during one of his cross-country leaps...and for obvious reasons, it's often an important factor for citizens in and around NYC.
Short version: Stuff gets trashed by super-fights, but it's just one more risk in life like **92** drivers or heart attacks (though the super-fights are usually more visually spectacular). Figure out if you can deal with those risks, knowing that much of the damaged stuff can be replaced or restored.
Post-Traumatic Stress:Cap's seen plenty of strange stuff in his time...there wasn't a crazy, out-there idea that HYDRA scientists didn't try to weaponize. If you watched Cap's movie, he gets tech tips from Stark's dad (who almost had a working hovercar), then takes on soldiers with disintegrating rayguns and weird propeller-rocket planes. Oddball or advanced technology is not going to faze this man. The social changes might be off-putting, but his crew of buddies in WWII came from all across Europe, so I expect he'll be able to adapt to the cultural differences in time.
Short version: Cap should be fine. Until Bucky returns, anyway.
Thor:Most of this sort of stuff can be addressed by my earlier discussion regarding legal issues. I do believe that Thor's citizenship status does get handled by the Avengers legal team...I think one of the She-Hulk comics even mentioned something about visas for Asgardians. He's not working directly for SHIELD, but he is working with them in a sort of collaborative effort, so concerns about his access to classified stuff is no more problematic than the access granted to Banner or Stark. And in all cases, Fury's a pretty paranoid guy and usually steers them away from places they're not supposed to be. This is probably a very poor analogy, but it's like in spy movies or cop shows, when you have 2 agents or officers of equal rank but come from different countries, or intelligence agencies, or departments. While there may be some friction or "need-to-know" type problems, they're also perfectly capable of cooperating in a friendly manner, especially when villainy is afoot.
Short version: Thor's not being deported unless he wants to be.
The Rest:Again, the Avengers are not a military taskforce under SHIELD's authority. Nick Fury may have brought them together (in the movie/Ultimate continuity), but in the end they are not part of his organization. That being said, Hawkeye and Black Widow began the movie as SHIELD operatives (and they had been in those roles in the Thor and Iron Man movies, respectively), and I would be surprised if they left their jobs. In the comics (mainly 616, maybe the Ultimates too), the Avengers roster is filled with reservists--basically, people they have on speed dial in case a crisis comes up and the guys hanging around the clubhouse aren't up to the task. Spidey, the F4, several of the X-Men, and yes, Black Widow and Hawkeye are all on the Avengers reservist roster (and probably several others I'm forgetting). What's more, being an Avengers reservist is not in any way being a second-stringer; it's an acknowledgement that you've got your own lives to deal with, but are trustworthy enough to come help save the world when the team needs you. I expect this is the case with Natasha and Clint; they're going to continue working with SHIELD as before, but will show up when they're needed (and assuming the actors are available

).
Short version: Actually, Black Widow and Hawkeye are now the only SHIELD operatives that can also claim the privilege of Avengers membership. The rest of Fury's staff will probably be jealous of *them*. At least, until the Avengers are rushed to the front lines to face down the next big world-ending crisis.
Media Matters:SHIELD is not a secret organization--their missions generally are, though. Again, another analogy (though poor): they're like the CIA...everyone knows the CIA exists, where their main office is located, and some of their public figures. What the CIA is actually doing at any given moment, and why they're doing it, and who is involved, is another matter and almost never fully disclosed. The heroes of the Avengers (well, the ones that aren't active SHIELD operatives) are the public figures in this instance--SHIELD isn't trying to hide Cap or Thor from media attention. And the media (at least in the various versions of the Marvel Universe) have enough sense to not try and interview Iron Man while he's shooting energy beams at bad guys. There are issues with secret identities, but that's a whole other storyline...the superhero personas of the Avengers team are generally known and enjoy just as much fame (good, bad, and weird) as any other **29**. The main difference being that their fame is usually the result of taking actions to save the world (so it tends to skew positively).
Short version: SHIELD largely operates on the down-low, but the Avengers are media darlings, and everyone's actually pretty much okay with that.
Well, I hoped that help resolve some of those nagging questions. Now you can watch the movie and really enjoy it...have fun!
