We encountered module edit errors when updating to Joomla 3.6.3. Our searches on the issue lead us to a Joomla page indicating that the error had been reported and that it could easily be fixed by simply following the instructions below:

• Clear your Browser cache
• Clear your CDN entire cache (cloudflare or others)
• (optional) Clear your server cache

The reason for the error is that the new Joomla version modifed the moduleorder field replacing some html with some element target (the new code in core.js) but if the old core.js is still cache in the browser or CDN, the old code will conflict with the new and generate an error.