When David walks into the morgue, he finds a man with his eyes and mouth sewn shut. when he opens the man's mouth, he mutters "behind....you...". The man that imprisoned him is behind David. How did the man see the Crazy? His Eyes were sewn shut!
Actually, if you look closely (best seen when David's cutting the guy's mouth free) you can see that his right eye is still open, sewn over, but open.
The man knows that the crazy doctor is lurking around somewhere and would try to attack David. If David hadn't seen him already, then he's probably behind him.
For all we know, the doctor'd captured the sewn-shut man in exactly the same way, sneaking up behind him as he was checking the other sheet-covered body.
The Government tries to cover-up the Nuke as a chemical plant explosion. How on Earth would anybody believe that a chemical plant, which nobody remembers ever being there, had enough volatile chemicals laying around to create a nuclear-sized explosion by complete accident. And how will they explain away the radioactive fallout in the area, unless they're planning to keep the area restricted for the next 10,000 years?
That wouldn't matter, either. Every major country in the world would be able to analyze the radiation in the matter of months, and determine that it's origin was a nuclear weapon somewhere in the North-American continent. It wouldn't take a genius to count 2+2.
It's generally implied that it was a fuel-air bomb, not a nuke. So no fallout to be explained with that.
David and Judy are still a good distance away from Cedar Creek when the satellite sees them. Why do they immediately resort to quarantining the city on the mere suspicion that the two of them are infected, rather than sending a helicopter around and gunning them down before they reach the city?
Setting up a quarantine after they've gotten there would probably take too long. It's likely that there was a helicopter on its way to intercept David and Judy: if it succeeded in stopping them before they could come into contact with anyone else, the quarantine could be lifted before it progressed to the Kill 'em All stage.
The general consensus is that the military intended to kill everyone anyway and the evacuations were just a trick. There are a few questions to raise on that, number one being why they didn't just nuke/fire-bomb the town from the start? They went through all the trouble of setting up a medical examination center, separating infected from non-infected, taking blood samples and the like, bringing in outside help (there were several EMS units at the truck stop) and creating who knows how many witnesses (even the soldiers wouldn't stay quiet forever, especially on something like that), not to mention exposing more people to the virus, when they were planning to just kill everyone anyway?
If you're less attracted to the Humans Are Bastards trope, you could argue that the initial intention was to save whomever they could, and the decision was handed down to kill everyone once their initial data on the townsfolk revealed just how much of a threat the contagion posed. If you're fond of that trope, one could just as easily argue that the entire incident was no accident, but was contrived purely as an excuse to test the contamination's effect on an unwitting population. In which case, the nuke-it-from-orbit option would've barred their data-collection efforts.