Common.js runs in all pages. It assumes a lot of things: that a skin is fully loaded (see T86850), that the sidebar is visible, and so on. It applies changes to articles and common special pages, but ContentTranslation is a very different special page - practically no skin, no side bar, no usual elements, and so on. The only significant element that it has in common with other special pages is the top personal bar.
Common.js can run conditionally using
mw.config.get( 'wgCanonicalSpecialPageName' ) === 'ContentTranslation'
But maybe it's even better not to run it on ContentTranslation at all. There is a precedent for this already - MobileFrontend has its own JS file.
This issues already caused problems in es.wikipedia and eo.wikipedia, and may cause more issues in other projects where CX will be deployed in the future, so we should think about this soon.