Are you sure that these images are send with a proper MIME type for images and not with a generic MIME type that makes Firefox show the "Open with" dialog?

You can look at this extension:

• Open in Browser: https://addons.mozilla.org/firefox/addon/open-in-browser/

I don't understand what MIME type the image possesses. I need to point out that not all JPEG images have the same problem. For example, this can be opened in Firefox normally, but this just never yields.

I fiddled around with Applications of "JPEG Image (image/jpeg)" and now the problematic jpg file is always opened in "Windows Picture and Fax" and ignores any other action I have chosen.

That second image that gives a open with dialog is send as Content-Type: unknown/unknown and the first working image correctly as Content-Type: image/jpeg
So this is a problem with the configuration of the server and you would need the above mentioned extension to override this.

data:text/html,<img src='http://static2.wikia.nocookie.net/__cb20131209145630/megamitensei/images/6/61/Persona_4_the_ANIMATION_-_15_-_Large_30.jpg'>

I installed the extension, but now Firefox always opens the JPEG in question in "Windows Picture and Fax Viewer" even if I've set "Always ask" in Applications. I think I've hit the bug of Firefox handling file of unknown MIME type.

Try to delete the mimeTypes.rdf file in the Firefox profile folder to reset all file actions.

• http://kb.mozillazine.org/mimeTypes.rdf
• http://kb.mozillazine.org/File_types_and_download_actions#Resetting_download_actions

Note that the extension will allow to open this image file in a Firefox tab as that is the purpose of this extension.

OK, finally solved, although not the way I have hoped. Undeniably it is a bug that should be fixed instead of relying on an extension.