In terms of the science, I just have to accept that "mutant" is a license to do whatever you want, biology and physics be damned and I'm not complaining when it looks so cool. What I did find curious though was a bit of genetics in the film in which a character said they could detect people who could have mutant children or have grandchildren that could be mutants. This got me thinking, the films and comics often refer to a gene called the "x-gene" which seems to be the super awesome gene that results in all the mutant powers. I'm guessing it must be a transcription factor. The fact humans can have mutant children means the mutation is either spontaneous (a random mutation in the parent's germ line) or recessive (the mutant has to have two x-genes to be a mutant). But the grandchildren thing strikes me as odd because if it is recessive then you wouldn't necessarily have to wait an extra generation to get the mutant child. Unless two separate recessive mutant genes are required eg "x-gene" and "Z-gene". This might help explain why the mutants are so rare as well as the major variety in powers (maybe the other Z-gene encodes an epigenetic remodelling factor?).
That or the screenwriters didn't really consider the genetic implications of that sentence. In true Marvel tradition I'm providing a "no-prize" in case they need let off the hook.
If the genetics didn't make any sense on first read, hopefully this diagrams will help. Be warned it gets far too geeky from here on out.
Scenario 1 : both parents carry the recessive "X-gene" and you need two copies of the "X-gene" to be a mutant
In this scenario there's no point looking at one of the parents as "human" as it would mean none of the children would be mutant. There is a 25% chance that a child would be normal (black cell) or mutant (green cell)There is a 50% chance that the child will be like the parents in that they aren't mutant but carry the "X-gene" (blue cells). I should note this is maybe what they meant by "grandchildren" but it seems redundant when the a mutant can occur in the first generation.
Scenario 2: mutants need to be homozygous for the "x-gene" and "z-gene"
In the first generation from "grandad" it doesn't matter whether his wife was a mutant herself, none of the children would be mutant as Grandad cannot provide a copy of the Z-gene. A quarter of potential children would carry two copies of the X-gene and one copy of the Z-gene (red cells), while half would have one copy of both genes (blue cells). Depending on who the red and blue children mated with the grandchildren could indeed be mutants.
For the next generation, let's take one of the "blue" children, wait for them to grow up and then pair off with another adult. For this generation the opposite sex still needs to be an individual carrying at least on copy of both "mutant genes" for there to be any chance of mutant children. So let's use a "red" individual (not a Sibling - this isn't Game of Thrones!) and see what happens.
As you can see there's a 12.5% chance a child from these parents will be a bona fide mutant. Even more worrying for the likes of Bolivar Trask is that there is a 62.5% chance that this couple will have children who can provide at least one copy of both genes - meaning all of these individuals could have children that are mutants too. Now you can see why a maniac may go so far as removing people whose grandchildren could be mutant.
And for any of those wondering, it means that Quicksilver's mum must have been carrying at least one copy of the X and Z genes. With Dad being Magneto there's a good chance that his sister is a mutant as well :P