@AKlapper (WMF), my first step for diagnosing is asking user to test while logged out, or in incognito window to reduce the hassle. (How) is that different from the safe mode thing? If it is, it is worth adding somewhere?
Topic on Help talk:Locating broken scripts/Flow
@Elitre (WMF), if I understand https://phabricator.wikimedia.org/T152169 correctly, safemode also bypasses your browser cache. Might be a question for the developers involved in that task?
safemode doesn't run any of personal user scripts, gadgets, or sitewide JavaScript in the MediaWiki namespace, e.g. MediaWiki:Common.js. Logging out will still run default gadgets and sitewide JavaScript in the MediaWiki namespace. I think this difference should be mentioned. If safemode stops a problem but logging out does not then it may be a waste to test your personal JavaScript and opt-in gadgets.
Another thing worth mentioning: If you preview a personal JavaScript page, e.g. your common.js, then the previewed version runs instead of the saved version. If the issue can be seen on the previewed page then you can make tests without saving all the time.