Hi Joseph,
I think I figured it out for the major browsers. But even with these changes, it's still happening in IE11. The changes I made were related to the webmap's json. You can edit the webmap json using AGOL Assistant. There were two edits that I made:
1. I took out all field references in any popup's display field. Sometimes the display field references old fields from the service that are no longer available, and that messes things up.
2. I cleared out all layers that were only defined by just the id. So something like:
...
{
id: 3
},
...
I took all of them out of the webmap json.
After those 2 changes, we don't get the untitled layers in the Layerlist for major browsers (excluding IE11, where it always happens).
Hope this helps you