There is a setting under Site administration>Development>Debugging

Show origin of languages strings
$CFG->debugstringids
Default: No
If enabled, language string components and identifiers are displayed when ?strings=1 or &strings=1 is appended to the page URL.

It does not work for the content that is loaded via AJAX because obviously there is no "strings" parameter passed to them.

This has been also reported in MDL-62439 and fixed for one single case (help popup). Now there is more and more AJAX-loaded contents in Moodle and it will be impossible to pass parameters to all WS loading contents.

Example:

• Enable $CFG->debugstringids
• Go to calendar and add "strings=1" to the query string, your URL will be something like this https://YOURSITE/calendar/view.php?view=upcoming&strings=1
• You can see all string ids, that's great
• Click on "New event" button
• You can no longer see string ids in the dialogue

Apart from the modal forms there is a lot of pages that have content loaded dynamically. In core there is at least report builder - check out something like this /reportbuilder/edit.php?id=14&strings=1 , in Workplace pretty much everything is loaded dynamically.

We clearly need to find a different solution to enable/disable showing string ids, maybe something similar to turning editing mode on and off.