iPhone, is it possible to recover only one app from a backup? The latest release of an app I love is completely buggy.
Can I recover it from a backup without recovering everything else?  

My last backup is quite old :-(
You can't recover from an iPhone backup, but there is other way.

You can check your apps directory within you iTunes Media Folder Location (under iTunes → Preferences → Advanced). This will tell you where your iTunes are located (example: /Users/username/Music).

If you go to /Users/username/Music/iTunes/Mobile Applications you can find that this is the directory where apps are saved.

Check this folder to see if the app you are looking for is there. Apps have version number in it's name. If not exists what you want, or exists the latest version, you must use a backup to recover (If you have it).