At my last code review question I added a tag related to the programming language itself. Are extra needed? I think so.
We are actively trying to reduce "meta tags". For example, see: Optimize our meta tags?
Tags are expected to summarize the content of the code in the question. They are not expected to summarize the desire of the question asker.
readability is a meta tag - it indicates that you want your code to be readable, it does not represent what your code is, or does. Also, we would expect all code reviews to address the readability of the code, so the tag would not add value.
The compatibility is similar in the sense that it is something you want the reviewers to inspect, not something that the code specifically deals with.
Note that just because we allow 5 tags on a question, does not mean you should feel pressured to add 5. It's OK to just tag with the language.
In summary, neither tag is a good one for Code Review.
If you want reviewers to pay special attention to readability or compatibility, then add a comment in the description expressing what your concerns there are.