jpeg file format decoding
I had a similar problem years ago with some PNG code (though I didn't write it from scratch). It turns out my code was more standards compliant than the libraries by Windows, some browsers, etc. They did fine on typical cases, but choked on unusual and contrived images, even if they were completely in line with the standard. A common way to trip them up was to use an odd pixel width for the image. Almost half of my test suite was not viewable with Windows. (This was many versions ago, like Windows 95. The Windows codecs have improved substantially.)
I ended up building the open source PNG library and using it as my reference implementation. As long as the images that my code produced could be parsed by the reference implementation and vice versa, I called it good. I also checked that my code could display any image that Windows could display. Every time I found a bug, I added the image to my test suite before I fixed it. That was good enough for my project.
You could do the same. I believe there's an open source JPEG library that's widely used as a reference implementation.
If you really want to figure out why Firefox (or whatever) cannot open your image, you could try starting with an image that does open in Firefox. Incrementally make small changes (e.g, with a hex editor) to make it more like the image that fails. That might help you narrow down what aspect of your image is tripping up the application. Admittedly, some of those steps may be hard to try.