Some commands -- the ones in editMenuOverlay.js that were changed by bug 371900 -- are special in that they have a key/menu defined in the <keyset> or menu, but the actual key handling behaviour is done via the ones in ShortcutKeyDefinitions.cpp. To accommodate this before patch 371900 there was a special-case that would ignore keys that didn't have a command or oncommand associated with it, however there are cases where you want to use an event listener defined separately. So, now, post-371900, those key elements are not ignored so nothing will happen.
Instead, you need to add internal="true" to those keys. For example, I tried adding internal="true" to the key "key_selectAll" that is defined in mainKeySet.inc.xhtml and this allowed the test browser_attachment.js to now pass.
There seems to be quite a few different files where this key and others are defined with no associated command handler, so I assume fixing all those up would fix these tests.