I have a feeling dropins.js conflicts with mootools because I'm getting a Javascript error when trying to use Chooser.
The button is inserted using
document.getElementById("DBContainer").appendChild(button);
After I click the button the items are loaded, I can select them but clicking cancel or choose does nothing.
If I close the dropbox pop up window the cancel function still runs.
Uncaught TypeError: JSON.parse is not a function
From the error message, it seems that the issue is that JSON.parse is not set to a function. The Dropbox Chooser functionality does use JSON.parse, and that should be available built-in to the web browser as that's a standard function included in web browsers.
I can't offer support for mootools or any other particular third party library in particular, as it's not made by Dropbox. If there's something that's removing or replacing JSON.parse though, I suggest refer to the documentation for it to see how you can avoid that, or otherwise not use whatever is doing so.