We have a large part in our code base that was never reviewed and has a lot of flaws. As every tool I know only allows code review by pull request, is there any tool to review an existing code base, so that we can comment on every line?
Crucible (like user246 suggested) seems like a tool which has the functionality you are looking for. I have used it in the past to review commits and not pull requests. I think you can also assign parts of code.
Alternatively you can have a look at the open-source Review Board which supports multiple ways to create reviews, from commits, hooks or even dragging files. There are more alternatives: http://alternativeto.net/software/crucible/
Code quality can also be viewed/measured with a static code analyses tool like SonarQube:
SonarQube: Put your technical debt under control
This might result in which parts might need reviews and or refactoring.