This is a trivial one, I know.
It is possible to create multiple categories with the same name and/or same slug, and doing so breaks all concerned categories.
To recreate:
1. Go to Manage -> Categories in the admin panel.
2. Create a new category.
3. Create another category with the same name and/or same slug.
4. Place some posts into these categories (so they show up on the blog) and then attempt to browse one of the categories via the blog. A 404 Not Found error is returned on all categories concerned.
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Desired Behaviour:
Either the user is alerted that they are attempting to create a duplicate category, or the duplicate category is created with a numerical suffix on the slug (eg. articles-2) much the same as is done with multiple blog posts that have the same titles.
IMO the first option would be preferable.