I know it's not literal, but is it really incorrect to say, "ti år er gået" ? I have heard the verb "gået" used in this context quite often.
No, "gået" isn't incorrect at all! I would say it like that. I've never heard someone say "x år er passeret", at least not in Copenhagen and its surrounding areas. I suppose both words work, but I would never use "passeret" myself.