The physics major inside me is begging to speak here.
The flaw in this idea is that, when we touch something, we are not actually touching it - that is to say, the particles of our body are not colliding with it in the same way that one pool ball collides with another.
Instead, the electromagnetic force makes the electrons in the outermost layer of atoms in your body repel those in whatever you're touching. As I type this writeup, my fingers move towards the keys. Eventually, the outer layer of the electron cloud around my skin (or, rather, the oil on my skin) gets close enough that it exerts enough force on the key to overcome the resistance in the spring under the key. Actual touching is not needed, and indeed it the size of an electron is impossible to measure since (among other reasons, which involve quantum mechanics) we can only measure the size of the area in which the force exerted by the electron measures more than a specific amount.
Thus, if one attempted to walk through a wall with any degree of speed, one's atoms would be repelled by those in the wall. The problem is that walls are made of materials which resist deformation far more than those which make up the human body (which is largely components suspended in liquids). This would tend to lead to an injury, as most would expect.
How the electrons and atoms 'line up' is not relevant. However, it is interesting to note that atoms of hydrogen can pass into of certain metals, simply because the hydrogen atoms never get close enough to the metal atoms to be strongly repelled. This is one of the methods used, IIRC, to make absolutely pure hydrogen, and is also a consideration because the interaction between the hydrogen and the metal of the tanks used to store it can weaken the metal.
If the monk nevalnin mentions did somehow get halfway through a wall, part of the wall would certainly not vanish, providing a space for him to be trapped and smother to death. I don't know enough to know for sure what would happen, but my best guess is that the material (both body and stone) in the area of overlap would expand greatly, causing the wall to shatter, possibly explosively; the reason that dynamite is used in blasting rock is that, when ignited, it produces a large amount of gas, causing a similar outward force.
There would not be a nuclear explosion, simply because very few of the atomic nuclei would be close enough to fuse. This might, however, be a very major concern if a large party of monks, walking through the same section of a wall, were to "lose concentration".