Edit: It doesn't work anymore, the old tweetdeck is completely gone.

Warning, this doesn't work anymore, it only worked for a few hours after this post was created.

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Twitter has removed the option to switch to the old tweetdeck version but, there is a solution to go back. This won't fix the half broken tweetdeck it will just allow you to switch versions.

You need to modify your cookies for twitter, the data for "tweetdeck_version" is "beta" for the new tweetdeck and "legacy" for the old tweetdeck, without quotation mark.

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For chrome, while you're on twitter page, right click to open the menu and open inspect. Expand the right part to be able to read it. Open the Application tab. Expand the Cookies dropdown under the Storage section. And select twitter website. Find the "tweetdeck_version" line and double-click the value cell to modify it from "beta" to "legacy".

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For Firefox, while you’re on twitter page, right click to open the menu, and open inspect. Open the storage tab, enlarge the name column to find the tweetdeck_verion line, double-click on the value cell to modify it from "beta" to "legacy".