I actually like that 1979-1981 timespan for a lot of settings. It seems just enough after Disco and before glam rock, out of the ridiculousness of the 70s enough but not fully into the worse ridiculousness of the 80s. It's a genuine time, man. It's that Wet Hot American Summer (2001) time. It's perfectly Spielbergian - most of us were little tots or at least little spermies at the time, just squirming around sandboxes/testicles waiting for the world to give us a chance. It's before the greed and insanity of the 80s started (highlighted here and here) but after the coke fueled nonsense of the 70s (here and here). Every time in history at some point in history is referred to as the time of innocence (except the 1340s and the 1710s) but this one really nails it.
So there are tons of obvious homages to Spielberg here, from the tonal viewpoint of a kid (by the way, all of the kids are pretty good actors, they sell their friendship spectacularly), parental issues (One my favourite readings of Jaws  is that of a story of male impotence, citing Brody's struggle for the approval from Quint and Hooper as substitute parents) amidst a fantastical backdrop (A monster). J.J. Abrams himself has less of a distinctive style. Super 8 is only his third directorial effort after Mission: Impossible III (2006) and Star Trek (2009) and the only major element connecting all three is the prevalence of lens flares. I don't think I can think of a better description of Super 8 than "Spielberg with Lens Flares." That's how you get Abrams. I think people tend to think Cloverfield (2008) when they think J.J., which was his production but not entirely his effort (tho all his non-franchise efforts like Super 8, Cloverfield and LOST seem to have easter eggs among them, like Slusho machines everywhere). There is certainly a bit of Cloverfield here in some similar mysterious dangerous monster running amok through town but Super 8 tends to be far less gimmicky.
There is this very unique mystery throughout Super 8, something vacant in other contemporary blockbusters. I think the E.T. (1982) vibe wears off however when the Alien starts killing and eating people. He's really not all that sympathetic as the ending makes him out to be. That's all I want to say about the ending actually, there is a genuine mystique to this movie that I think is preserved only by viewing it in a 2-D theater. 2-D is the only way to experience this movie! Wha-hey!
The government conspiracy stuff is played pretty heavily and they're the major baddies here. The military actually hasn't been this unilateral evil in a movie recently, we've almost gotten used to the Michael Bay Hero Treatment. The anti-government paranoia and mistrust is obvious in a post-Nixon / post-Vietnam setting when the American populace was really on edge for what the Feds might be up to next (And who can blame them for their weapons going off and killing everything in sight, even if it's the Alien's fault why didn't they unload their guns or stop driving or anything?). This plays well here. Super 8 is actually notable in that it is really a "Slice of Americana" small town story that has some universal truths, so universal that a plucky small child can connect with a violent murderous alien. 'Nuff said.
And I feel like I'm the only one who noticed this - what's up with Mr. Woodward the Mystic Negro? It's not really the worst possible use of the trope but you get the feeling that this scary black guy was the only one who really understood the Creature and no one else would listen to his Magical Wisdom. He's also the only black guy in the damn film and ostensibly the most intelligent.
The last thing I'll mention is The Case (1979), the kids' completed film we get to see during the end credits. It may be the best part of the film (only if because it's the driving force for most of the kids' early motivation. And late motivation in some cases).
Praise to people wanting to be Spielberg.