Indeed, your Tag archive URLs seems to be generating an Error 404 response (the error404 class in getting printed to your body and article HTML tags). So you’ll need to do some troubleshooting…
Is the problem theme related?:
Try quickly switching themes (during a time the site how low-use, or on a test site — if you have one). If that corrects it, then: Did you make any change to the theme’s code? If not, then post your question o the theme’s support forum.
Is the problem plugin related?:
Try disabling any plugins that might be Tag-related. If that doesn’t fix it, try disabling all plugins.
Is the problem Permalinks related:
I noticed you changed the default permalink Category base setting from “category” to “kategorie” (in Dashboard>Settings>Permalinks). Is the default Tag base still “tag”?
Just for more info:
Try adding the Tag Cloud widget and see if those links are the same non-working ones.
That’s alI can think of for now.
