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You could just open two windows and put them side-by-side.
I'll see what I can do. Maybe this should be the default behavior. I think TextMate does it that way.
Currently, you can do a right-click on the tab and select "Move Tab to New Window". This options only appears when you have at least two tabs in the window though.
What about folders? Is it ok that a folder is added to sidebar in the current window?
By the way: that kind of feedback is very helpful. I had to make some decisions when implementing the sidebar and it's good to know how other people would like the app to behave.
Regarding the video: if you had double-clicked the file "setup.py", it would have stayed open and it probably wouldn't have been so confusing. Doing a single click opens it "transiently" so that you can quickly navigate a folder without opening many tabs. The transient tab is closed as soon as you open another file.
I like to work with only one window, so maybe it should be added as an option. I'm not sure how to name that option though. "If you have opened a folder, opening additional files outside the tree should utilize a new window." is a bit long :)
The untitled document is closed automatically once you open an existing file (as long as the untitled document isn't modified).
This sounds like a good idea.
Did you try to use the list of recently opened files for this? http://www.textasticapp.com/v4/manual/lessons/How_can_I_show_a_list_of_recently_opened_files_How_can_I_close_the_current_file.html
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This problem should be fixed in Textastic 2.0 which is now available on the Mac App Store.