In ArcGIS web map viewer, the save button does not indicate that pending changes to the map have not been saved.
- Web map save button before changes:

- Web map save button after changes:

In Web AppBuilder for ArcGIS and most ArcGIS configurable templates, it is possible to see if there are unsaved changes in your map/app.
- WAB save button before changes:

- WAB save button after changes:

There is even a message to let you know that your changes will be lost if you close/refresh the browser page!!

Could we also have this for the web map viewer? 