There is currently an issue with uploading files via the visual editor. With our recent change to using Amazon S3 for file storage, uploads from the visual editor do not work. Until this is resolved, all uploads must be done via the Files page.
Tip: Immediately after you upload an image via the Files page, click the Path button in the upper right corner of the page. The path to the image is copied to your clipboard. Then you can switch to the page with the visual editor (we like to do this in another tab, so we can keep the Files page open) and paste the path into the URL field in the visual editor's image dialog.
We plan to entirely replace the visual editor, rather than simply fixing this issue. The good news is that it will be much improved editing experience when we are done. We expect to launch the new editor and file upload interface soon.