Error Message: <span> vs <label>

Assuming you mean an error message associated with a specific form control, use a <label>.

The semantic arguments are subject to debate, as they aren't clear cut in this case, but the practical arguments win quite nicely. If a screen reader is in forms mode, it may skip over non-label text thus hiding the error messages from the user.

Either can be used and both can be styled. I think the discussion will be about symantically which is more clear. I think of label elements as being associated with describing what a particular input element's intent. I don't feel displaying error info fits this and prefer the span.

AFAIK, the purpose of a label is that clicking on the label clicks the control that it is "for". This is very helpful for things like checkboxes and radio buttons, where the actual control is small and tricky to click.