Yes, some were probably aware. I don't know anything that says it directly in canon, but I do know that there are these things said here in my following points that are based on canon.
In Chapter 1, of the Half Blood Prince, The Other Minister, Cornelius Fudge talks to the Prime Minister. From this interaction we can see that the 2 of them have met before and it is Fudges or other Minister of Magic's jobs to talk to the Prime Minister and help him understand and fathom what he is told and what happens.
On page 9 of that same chapter:
.........but the Department for the Regulation and Control of Magical
Creatures tells me that it's down in the rule book that we have to
notify you if we're bringing highly dangerous creatures into the
So from this qoute it is obvoius that the Prime Minister is told things, he doesn't have to tell other muggles(I don't think), but it is likely he tells or told a slight few people.
Since Voldemort took over the Ministry the Prime Minister probably isn't being told anymore. That means the only people that know are probably some people that have magical relatives or people that are somehow getting info or know about magical people. The Prime Minister probably didn't tell much of anybody what he did know, because then it would have been on the news and he would have been kicked out of the office for being crazy, it also might of put people into a panic. No one would have probably believed him.
2 If no one told the muggles then they either knew or extrapolated or stayed painfully dumb. But in Chapter 1 of the Half Blood Prince it is documented as saying that Fudge told the Prime Minister a awful lot, that means that the Prime Minister probably deduced that a war was coming.
He was told that:
a). A mass breakout occured from a high security prison holding very deadly people
b). The guards to Azakaban left and were breeding
c). Voldemort a powerful wizard that they told him was dead is in fact alive
d). The Ministry can't control their own people
All in all, there is more but just those facts that show that this is a breakdown of society that will probably lead up to war as more and more events similiar to these happen. And the Prime Minister knew it.
Chapter 1, page 18 of Half Blood Prince
"The Prime Minister gazed hopelessly at the pair of them for a
"But for Heaven's sake- your're wizards! You can do magic! Surely you
can sort out- well- anything!"
Scrimgeour turned slowly on the spot and exchanged an incredouulous
look with Fudge, who really did manage a smile this time as he said
kindly, "The trouble is, the other side can do magic too, Prime
- This new point is basically about the rest of muggle society, they the muggle society probably didn't know all the juicy details that the Prime Minister knew and he most likely didn't tell them as there was no widespread panic.
I mean there was food on the shelves in the grocery store and that means that people hadn't abandoned there jobs and holed up in their houses. Or the shelves weren't emptied as people ran around trying to mass stock food.
Chapter 16 Godric's Hollow from the Deathly Hallows
"Hermione had been to a supermarket under the invisibility
coat(scrupulously dropping the money into a open till as she
Also, people weren't openly fearful so few knew about a war.
I mean if you are in the middle of a war with people that do not like you and can be invisible and can do other "talented things", then you wouldn't exactly be hanging around doing nothing and making a target of yourself. But then again maybe they were religous and maybe they thought they were safe. Or they didn't know anything.
Chapter 17 Bathilda's Secret Deathly Hallows pg. 331
"The pub was fuller that before: Many voices inside it were now
singing the carol that they had heard as they approached the
And they dressed their houses up. I mean a lighted window probably draws attention that somone (probably muggle) is using electric(who else uses electric). Either way someone is going to check and if you know that people are hunting you or a war is going on, you wouldn't do this. The muggles know what the wizards are capable of, while they don't know they exist. They can see unexplainable events happening that are dangerous and baffling.
".... past more windows sparkling with multicolored lights, the
outlines of Christmas trees dark through the curtain."
- Even though few people knew about the second war, everyone would know after a while, maybe months, maybe years, but they would definitely know. The ministry with Voldemort in control was basically for putting pureblood wizards at the top of the world and that meant making everyone else bow before them and probably die.
Remember the quote "Magic is Might" on the statue in the Ministry of Magic building.
From the Chapter Magic is Might, Deathly Hallows
"....what he had thought were decoratively carved thrones were
actually mounds of carved humans: hundreds and hundreds of naked
bodies, men women, and children, all with rather stupid, ugly faces,
twisted and pressed together to support the weight of the handsomely
"Muggles," whispered Hermione. "In their rightful place.Come on, let's
Also, in the Half Blood Prince, the Prime Minister might have been imperiused later to not tell anyone, as Fudge in that book had to give him guards and one of his employees were still imperiused. This assumption is probably wrong though, Kingsley probably told him not to.
Chapter 4 of Deathly Hallows, The seven Potters
"Kingsley, I thought you were looking after the muggle Prime Minister?
he called across the room."
"He can get along without me for one night," said Kingsley, "You're
Few muggles know, as noone told them and there wasn't mass panic. It is impossible for noone to have known as somebody always knows something(there are at least 7 billion people in the world 4-5 of that billion are probably muggles, possibly 6 billion). But I mean people that were'nt spirited away like Hermione's parents and the Dursley's, people like Nymphadora's father (he canonly knew) had to have known and possibly muggles who believe in "magic" and are considered wacko by all the other muggles had to know something was up. Also, the Minister probably knew if the Death Eaters didn't get to him.
A explanation of other occurrences
As you mention the dragon, yes people probably knew that things weren't "normal". So the Ministry after the war probably made it all look like a hoax and did massive mind-wipes. Like the Dementors they couldn't see them so they couldn't give a direct reason, that might have been the case with the Dragon and other unexplainable events. I think people program their minds to believe what they want to believe, also the Ministry section that deals with Magical Creatures would have probably dealt with the dragon.
Muggles that knew of the Second War:
And a very few Muggle citizens