I'd love to be able to have three or more lists open, see them all as tabs, and switch back and forth with a single click . . . just like a modern browser.

And I'd *really* love to be able to save a configuration of which set of lists open upon startup . . . just like a modern browser.

ActionOutline has tabbed lists, but not the "homepage" configuration feature. For me, it's your closest rival.

In color settings I should be able to select a color theme, like Zenburn, Solarized, Dark, where whole UI will be perfectly polished, to work with that theme.

When in a design meeting, freeform editing like in Checkvist is very useful, but it's a lot of work to copy and paste Checkvist text into the issue tracker. Exporting directly from Checkvist would be awesome. The "highest level" task should be the issue title and the child tasks should be added to the issue description.

Exported tasks should be clearly marked and link to the corresponding Jira / Youtrack issue.

An excel-esque shortcut for current date [ Ctrl + ; ] and current time [ Ctrl - : ] would be useful

something like... http://online-stopwatch.chronme.com/

On a mobile device, my primary use is to actually DO things on the list, so after I do them, I want to easily check them off.

It would be great to have a calendar view of the current week (or day, or month) next to the checklist (where the keyboard hints are currently displayed) and being able to drag and drop tasks into the calendar.
This calendar view would be awesome to schedule your day and week based on your priority, and have a quick view on what needs to be done today.
If you couple that with Google Calendar integration and a full iphone app, you've got yourself the dreamiest organizational tool of all times!

How it must work: when i open the website page i click on Chekvist app icon and attached to current URL (or just domain) list opens automaticaly.

I have 27" Thunderbolt display and Checkvist takes use only tiny amount of screen real-estate. Could there be a full width mode for people like me? I also take quite lengthy notes so extra width would be a help.

If I have "Show as a numbered list" turned on, and then I export to plain text, the export should include the numbers.

Be able to highlite an image and add it to a list using the 2Checkvist button.
Also be able to past a link URL and have it automatically converted to an image

Allow me to set the styling for an outline. Looks like there are fairly limited elements -- three fonts, line spacing at perhaps three levels, and indent spacing(s). Might also allow the expand/contract symbol to vary.

I consider this quite important, as I'd like styling to squeeze more on a page, with tighter spacing and smaller fonts. Web 2.0 sort of styling is nice for presentation, but not so practical for working documents.

the way Google Docs does.

I really need the ability to list any predecessors a task has... or to put it another way, I need to record the tasks that a certain task is dependent on. I have been evaluating veoproject, which allows this using task id numbers that are autoupdated as the task list is altered) but I like your interface better so I hope you will add this!

Helps with natural language entry (e.g. #do research for project)

This makes lists always available, and is the only reason I'm sticking with gubb.