Many of the add-on's functions do not work, including all of the drag-and-drop functions.

This sounds like a couple different issues. The drag and drop problems might be related to bug 936092. For those following at home, here's a link to this add-on on AMO: https://addons.mozilla.org/en-US/firefox/addon/tile-view

From the developer, here is the current status: not started updating yet, but this should be simple once updating of Tile Tabs has been completed, since Tile Tabs and Tile View are based on very similar core code. Marking as a dependency of the Tile Tabs bug.

It looks like both add-ons have been updated to support e10s. dw-dev, can you please confirm?

Both Tile Tabs and Tile View have been updated to work in e10s windows. Tile Tabs has been compatible with e10s since version 12.0 (2014-12-24). Tile View has been compatibe with e10s since version 4.0 (2015-1-20). However, for both Tile Tabs and Tile View, most of the drag-and-drop operations into, out of and between remote browser contents do not work, and are waiting on resolution of Bug 936092 (which is blocked on resolution of Bug 1075670). So, both add-ons are currently usable with e10s, but are not fully functional.

Okay, let's keep these bugs open until the add-ons are fully functional. Thank you for the update.

With those bugs fixed, is this now solved?

For both Tile Tabs and Tile View, all of the drag-and-drop operations now work correctly, in both e10s and non-e10s windows. This bug can be closed.