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What I miss

keyboard shortcut to directly search without the need to use the mouse
I would like a keyboard shortcut to open a search field where I can just start typing and use the arrow up/down and enter key to open a bookmark, tab, folder.

search with more than one word
If I have a tab named: "TabsFolders | Exclusive Offer from AppSumo" -> a search for "folders sumo" should find a match

more keyboard support
e.g. hitting the keyboard shortcut for saving gives me a dialog -> but I can't save it with just by hitting enter -> I must change to the mouse
or when closing a window window with open tabs and the "save dialog" pops up -> just hit enter to save it and hitting ESC to discard it
or hitting ESC should clear the search also when the focus is NOT in the search field (in the Organize window)

a side note: I found out that CTRL+F brings the cursor to the search field (when you are in the Organize window -> GREAT :-) -> are those shortcuts documented somewhere?

show Organizer in sidebar
A separate Organizer window is great for the two panels and for getting things organized. But for just opening folders/tabs I would like to see the Organizer window permanently in a sidebar.

new tab Window shows Organizer as a default
This is something other extensions like Qlearly do and I think it would really be useful. You open a new browser tab or window and immediately see the Organizer :-)
If this would be possible an option would be cool to NOT keep the Organizer (a new Organizer window is just "a tab away" ).

support for many browsers and platforms
Maybe TabsFolders is not seen as a bookmark manager but a "session/tab" manager (which it does great - I really like the concept) -> but it would be inconvenient to have separate tools for that. So for me TabsFolders has also to be a good bookmark manager. One of the main selling point for bookmark managers is to be browser independent (unfortunately Firefox, Android and iOS are not supported at the moment).

web interface needs more features
This point could be (partly) a solution to the above problem (support more browsers and platforms).
At the moment we can only open single tabs/bookmarks via the web interface. I think there should be at least two other features -> "add new bookmarks" and "open folders (multiple tabs) at once".

open with "browser xy"
Wouldn't it be relatively simple to offer an "open with" option? So we would start the Organizer window in Chrome but could open folders/tabs via right click menu in a different browser like Firefox.
[ You can see that I really don't want to part with Firefox completely ;-). ]

(if possible I will submit a "part 3" with some minor wishes and ideas)