You will want to be selective with the categories and tags that you use. If you have multiple tag index pages with the exact same content you may be at some risk of serving nearly identical pages. It's still not a huge SEO issue as Google will likely just prefer one over the other.
If it does become an issue where multiple tags or categories are identical you can block indexing as you described.
Tags are primarily a feature for users to navigate subjects on your blog rather than a method to improve SEO.
The content quality and title of your posts is much more important in terms of optimization. We recently discussed ways to optimize content for search rankings just yesterday on our blog. I would recommend you focus on your content and keyword targeting as described there.
Hope this helps. Feel free to reach out if you have any other questions.