It's completely possible that the two missing rockets, which are actually one of the first things we are shown in the Fallout 4 trailer, could have a number of significant meanings.

First, we have the 'discrepancies' concerning the nuclear blast, which would in fact suggest that there were two. Second, as FoxtrotOscar has suggested above, they could also be a reference to our two missing family members, and the remaining one symbolic of the Sole Survivor. And third, as you have stated, they could be directly linked to whatever combat took place on the moon, as hinted at in the 4th July mural.

Watching the E3 footage actually reveals a staggering amount of information about this. If you watch very carefully, you can work out several map bearings from the compass at the bottom of the screen, as well as a number of relative distances. For example, if we take the billboard outside the vault, it can be seen https://youtu.be/D5esyZPt5Jo?t=10m7s, directly behind the blue 'observation pod' when we first leave the vault, and again https://youtu.be/D5esyZPt5Jo?t=25m22s whilst we are defending Sanctuary Hills. Note that in this last link, we can also see the start of the 'detour' we are made to take during pre-war, which actually leads due North-West directly towards the billboard.

All of this allows us to build something of a 'virtual map' for a number of the locations we have seen so far.

The misses were plausible. A friend of mine once said that nuclear missiles are not designed to be pinpoint accurate. After all, why would you need to be surgically accurate with a weapon that have a huge destructive power and range? Here is an example of a nuclear blast radius of a 500 kiloton nuclear weapon (although the missiles in Fallout would be of lower explosive yield, this illustrates the capability of a nuclear warhead):

http://i.imgur.com/ueyrL76.jpg

If the second warhead do hit Prospect Hill, wouldn't it also affect the Harvard uni vicinity, due to proximity? What is interesting, Harvard uni is likely to be the Institute's territory. Wouldn't that mean that the institute might do something about the warhead before it hit, like Mr. House? They are an organisation with highly advanced technology, after all. They would have access to anti-warhead defence system like what House had installed when the nukes hit...

EDIT: 500 kiloton is the yield of the strongest fission nuclear weapon, the Ivy King. Considering that Ivy King uses fission method, and is detonated in 1952, it would be plausible that the yield of the Chinese warheads in Fallout might be around that, or greater, as we don't know whether they still use the fission method, or the hydrogen system.

There is also a possibility that one bomb only hit the Boston area. If Mr. House was able to make a defence system that protected the majority of the Mojave.... why cant the Commenwealth/Institute do the same? The are supposed to have some of the best tech, the smartest scientists etc etc etc. I think it is entirely possible that only one bomb went off. Or maybe 2 hit, but one was a dud. Maybe it got hit by 3. Who knows?

I personally dont think that the institute and by extension the majority of the commonwealth area, would not have had some sort of defence system in place.

That's what might've happened to the bomb that is aiming the Boston naval yard, like what I've pointed out beforehand, as Prospect Hill (and by extension, the naval yard) is in proximity to Harvard university, an obvious territory of the Institute.

Current cep of the Minuetman missile is 200m. The reason why everyone was looking at building the high megatonage air delivered weapons had more to do with how inaccurate air delivered ordinance could be especially when it was parachute dropped to give the aircrew the ability to get out of the way.

Actually we are pretty sure that Concord is close to Vault 111.

AS for the crater in the artworks being close to the institute,that's true.

Don't forget the Glowing Sea

I actually have one or two interesting ideas about this...

I'm not sure if Harvard is part of the institute... I don't think they like each other enough... MIT is more about technology while Harvard is more about humane sciences. And they two don't like each other very much if I remember right...

Not say'n it's in the game, but, Physical Sciences, and "Human" Sciences could cross over in Synthetic Psychology; the motivations and interpretations of why Synthetic Intelligent machines do what they do according machine logic combined with trophic cascade driven reasoning derived from environmental inputs, data collection variables, and the hierarchy of decision tree matrices defined against previous experience outcomes.

Forgive me, but what is the "glowing sea"?

There is a building in the concept art that looks to be the inner 'courtyard' of Harvard University. Knowing what we do about the Institute and there central focus in Fallout 4, there is a very real chance that they have 'seized control' of all major learning centres in the Commonwealth, and so this would almost certainly include Harvard.

As a side note, Shanbalileh suggested earlier that if there were actually two detonations, then surely Harvard would have been destroyed in the Prospect Hill blast, especially given the apparent radius of damaged buildings we can see around the area of the crater. Well, I have an interesting theory as to why Harvard (as well as many other buildings in this area), would appear to be still standing, which I shall post up shortly.

See https://www.youtube.com/watch?v=DqQqeEgWb7Q interview.

It's the area near Boston that was hit by the nuke. Here is a picture: http://i.imgur.com/iMoV0eT.png

It took me a while to find it but I was sure I seen an image with two mushroom clouds on the horizon. It ended up being in the concept art at the beginning of the E3 Showcase: https://www.youtube.com/watch?v=D5esyZPt5Jo&t=4m54s. Though it may not be a nuke, there appears to be a third explosion.

The key point here is where this explosion happens.

Seeing that the Fallout world uses the kiloton atomics it would take more than two to take out the city and any other military and government assets nearby

There is no reason to believe that these MUST have been 'low-yield' nukes. We were setting off ten-megaton bombs in the early 50's.

See http://www.gamesas.com/topic/1526246-the-glowing-sea thread.