I have two pretty much identical Calamondins. One's graft seems to be fine:

But the other's does not:

Should I be concerned?

It will be fine.

if canopy gets bigger and bigger there could be a problem and it could breakdown the graft , after a while the tree will absorb the grafting point
I would suggest to put a little grafting tape along with 2-3 toothpics to make a tourniquet arround him.

First of all, I'm fairly certain that my PC caught a virus when I clicked on the ImageShack pictures to look at them in more detail!
Has anyone else had this problem - prevented any program from running and was quite difficult to resolve?

This is a cleft graft that has only taken on one side. I think it will be fine, although I would remove the small dead piece on the left and as much as you can of the right hand rootstock twig without touching the grafted part itself.

That second graft does look a little weak, I would support the top until the graft union has developed a bit more.

Maybe I should put some tape on?