Hi Andy,
I recommend using tags or categories not both on your WordPress website. You see, they are essentially the same thing. A Tag or Category will create an archive page once it the taxonomy is created. All posts or content that is either categorized or tagged with will display on the tag or categories archive page.
So if you have a post called Why I use Moz, and that post is categorized as SEO and Tagged as Best SEO Practices. You just created 2 new archive pages with the same post. Creating duplicate content. Now because these archive pages are in chronological order, new posts that are tagged and categorized using the taxonomies given above, the archive pages will always be duplicated because the content never differs.
To combat this use one or the other. I prefer categories. You will not get an extra SEO benefit for tagging your posts or categorizing them. This is for user experience and will have little effect on your ranking. However if you use tags and categories wrong you can get lower rankings for duplicated content.
Thanks,
Don