I'm not mainting this anymore. I'm using @eramdam's chrome extension instead: https://github.com/eramdam/BetterTweetDeck
The Tweetdeck Web App has stopped displaying inline image previews for tweets continaing Instagram links. This is probably to do with the great Twitter/Instagram war.
So here is some hacky Javascript to add Instagram previews back. I may get round to adding support for more image providers, like Imgur. And well, any type of image that ends in a valid image extension, why not eh?
For Chrome, install the Tampermonkey Google Chrome extension.
For Firefox install the Greasemonkey Firefox add-on.
Then add the tip.user.js file. If Tampermonkey/Greasemonkey is installed then you should be able to just one-click install from that previous link. Otherwise you may need to manually add the file as a new userscript.