How can a god, that apparently loves everyone, allow this kind of thing to happen?

[John V]

You guys should actually read up on the subject. You'll find that some people have indeed settled on the definition "able to do anything," but there are other views as well. Here's a good place to start.
http://plato.stanford.edu/entries/omnipotence/
IMO the Biblical use of almighty is closest to this explanation from the link:

A second sense of ‘omnipotence’ is that of maximal power, meaning just that no being could exceed the overall power of an omnipotent being. It does not follow that a maximally powerful being can bring about any state of affairs, since, as observed above, bringing about some such states of affairs is impossible. Nor does it follow that a being with maximal power can bring about whatever any other agent can bring about. If a can bring about s, and b cannot, it does not follow that b is not overall more powerful than a, since it could be that b can bring about more states of affairs than a can, rather than the other way around. For the remainder of this entry the discussion concentrates on this comparative sense of ‘omnipotence’ as maximal power. Within the context of that discussion, it will be assumed that it is not possible for an agent to have the power to bring about any state of affairs whatsoever.