I may have been too hasty to condemn the WordPress for iPhone app. One of my criticisms was that it couldn’t upload a photo to my site. Well, I just discovered that I couldn’t either, even using the browser. This appears to be another issue with WordPress 2.6.
Fortunately the fix is simple: fill in the otherwise optional Full URL path to files (optional) field on the Settings » Miscellaneous section of your control panel with the actual path to your images–usually http://yourdomain.com/yourwordpressdirectory/wp-content/–and save the settings. The forum doesn’t have a consensus on what caused this optional field to become mandatory, but that appears to fix it for most users.