What happened to the supervillains? What about the crime rate?
After the superheros were relocated there must have been a spike in crime. Supervillains must have seen that it was easier than ever to pull off crimes and gone on a spree. Why didn't this happen? If it did, what ended it? Where are the supervillains now - retired, jailed, relocated, dead? Was the Underminer a Golden Age villain or is he new? Do supervillains only arise if there are heros to combat them? Because it would seem logical to conclude the exact opposite.
Who designs supervillains' costumes?
It can't be Edna. Or can it?
Where do superpowers come from?
This is an issue which is not dealt with in the movie, for two very good reasons. Firstly, the movie isn't about the powers themselves, but how people deal with them. Secondly, to explains such a fundamental principle of your fictional universe is to take all the magic away from it. Look what happened with the whole midichlorians business in Star Wars.
But the question is there and I'm asking it. One thing we can firmly conclude from the fact that two supers beget three more supers is that superpowers are genetic in origin, somewhat like the situation in X-men. (Though, as an aside, it seems stupid to believe that a single gene, the X gene, can give rise to so many diverse powers.) However, it also seems that there is a hint of magic involved. For example, Jack-Jack turns himself completely into metal and instantly becomes many times heavier than he was before - this is impossible if you obey the law of conservation of mass. And you can't, you know, fling "coldness" like Frozone does. But whatever. Maybe some sort of technobabble can cover this.
At what age do superpowers manifest themselves?
Going purely on the movie, the answer would appear to be "almost instantly". Jack-Jack isn't even toilet-trained but the whole family firmly believes that he is without superpowers since he hasn't deomnstrated any yet. And consider Dash, with the power of super speed - tell me that name isn't a coincidence.
But when you watch the DVD extras you find out a little more. In Frozone's hero entry, for example, Frozone recalls being a young child at the time he first froze something; and there's also some hero (I'll check up on this) whose voice-related powers manifested while he was selling hotdogs in a stadium! So it seems a bit premature to assume Jack-Jack is without powers when he is only around 1 year old, when powers can in fact manifest at any time of your life.
That implies to me that the NSA, having seen what happened with Vi and Dash, did some kind of (DNA?) test when Jack-Jack was born and it came up negative.
But that raises further questions. Why did the test come up negative? What if it did come up positive but the NSA decided not to tell the Parrs? In that case, why would they withhold that information? Given that Jack-Jack appears to be by far the most superpowerful individual in the Incredible Universe it seems possible that there are more important factors here.
Where did all the Viper aircraft from Nomanisan go?
A host of Viper aircraft are seen landing at Nomanisan by Elastigirl as she sneaks in. But when she and the rest of the family return to the hangar later, all the jets have gone. At least one was taken by Syndrome as he flew to Municiberg to stop the Omnidroid 10, but where did the rest go? Were they escorting him? Where did they land?
Possibly they were rounded up by the government when they seized the rest of Syndrome's assets.
Why does Syndrome have two rockets?
What about Mirage?
Mirage is still alive at the end of the movie. She was last seen helping the rocket take off with the Parr family onboard. Presumably in the Syndrome-asset seizure she would have been captured along with everybody else on the island. But we never see this onscreen. And it seems entirely possible that she escaped. How does Mirage's story end?
What year is this?
It seems obvious at first that the movie takes place sometime in the modern era - or some alternate imagining of it, at least - but this is actually provably not the case.
Syndrome's computer entry on Elastigirl gives her last active record as being on 13th November 1955. That places the Incredible wedding sometime before 1955-11-13.
Some time later, Mr. Incredible is sued by Oliver Sansweet. Five days after that he is sued by the victims of the train accident from the same night. None of the newspapers which flash past during this sequence have visible dates on them, though the Municiberg Reporter with the headline "MR. INCREDIBLE SUED" has "Vol. 39. No. 99" visible on the right, whatever that means. This opens up a wave of copycat sues and I think it's reasonable to assume that this period of time took several years. That gives time for Stratogale to be killed in action on 23rd April 1957 and Thunderhead on 15th November 1958 before the Superhero Relocation Programme is put into effect and the superheros are swept underground.
That raises the question of what the events of "15 years later" are fifteen years later than. Luckily, Syndrome mentions that Mr. Incredible's attempt to bargain with him are "fifteen years too late" which implies that "15 years later" is specifically fifteen years later than the Incredible wedding, rather than fifteen years later than the end of the Golden Age.
It's never stated that precisely fifteen years have passed, but this seems a reasonable assumption. So the main events of the movie occur sometime in 1970 or earlier.
The architecture of the Parr house seems to reflect this and the director's DVD commentary bears this out; the Incredible Universe is apparently based on the 1960s crossed with the future that was imagined in the 1960s - i.e. jetpacks and island bases and suchlike. And while we can't put an exact year on the movie, we can at least give the new era of superheros a name; the Silver Age.