Plus:
http://en.wikipedia.org/wiki/CauterizationFire can't really handle non-lethal effects like knocking people unconscious.
Air might struggle with structural damage, breaking down doors/walls and objects that it can just flow around. It might also struggle to deal damage to heavy objects.
Water is similar to air, though it can use rust effects for damaging certain objects.
Earth isn't very subtle when it comes to damage. It's good with area effects, launching large boulders and things, pebbles aren't so effective though. Can't produce light.
Spirit can manipulate light and matter telekinetically, but it can't create any of the elements themselves.
With enough thought you can replicate most effects with any element, but some effects are easier than others. For instance you could use air to create sparks of lightning; or water could be used for a phosphorescent chemical perhaps; but it's not as good a light as creating a small ball of fire or creating pure light out of spirit magic.