For some strange reason I have a couple of Jpeg images that display about
50% of the time and 50% of the time they appear as "broken".

I've cleared the cache, tried IE7, Firefox and Chrome.

Same random results.

Is this a hosting issue?, a corrupted file issue, or something else?

I even tried uploading the file again under a new name but still same results.

Strange.

Any link for us to look at? Or any code to look at?

A link or code would help.

But, are you hosting these files on your own server? Or on someone else's? If someone else's it could simply be that you have a poor host.