Imgur has a nice API. I modified a ruby CLI for uploading images to imgur to fit my particular needs; you can find it at https://github.com/xiongchiamiov/limgur (or gem install limgur).
I believe you can also upload things pretty simply using curl, but I wanted to be able to generate bbCode thumbnails and such in one fell swoop.
Nope, but it'd be simply very useful to have at least some option to show file selector when I can put file path in my filesystem, because quite often I have that much more readily available than some option to drag and drop the file.
This is Carl, cofounder of Minus. Thank you for the suggestion, Ryan. We've been designing and iterating on an API and have just about finalized it. We'll implement this in a week's time or so, after we fix a few bugs first that folks on this list pointed out to us.