Can you open them from the downloads list, or do those fail as well?

Is there any pattern with particular kinds of files or download locations?

Start Firefox in Safe Mode to check if one of the extensions (Firefox/Tools > Add-ons > Extensions) or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance).

• Do not click the Reset button on the Safe mode start window or otherwise make changes.

• https://support.mozilla.org/kb/Safe+Mode
• https://support.mozilla.org/kb/Troubleshooting+extensions+and+themes

If "Open" and "Open Containing Folder" in the right-click context menu in the Download Manager window are grayed then that means that the file is no longer in the original download location and they may have been removed by Anti-virus or cleanup software.

its not dependent on the type of files. I can play the file from the downloads section. however, it doesn't show up in the folder, when I right click and click on open containing folder. its quite odd:( I tried changing the default download location too. same problem persists. i am forced to download the same file multiple times before it finally shows up in the folder

It seems to working well with other browsers. chrome, ie, etc.. when I download pictures and try to open it from the downloads window, it says that photoviewer cant open this image because its either deleted or in a location that isnt available:(

There is an interesting yellow tab above your downloads list which says "avast! Sandbox". I wonder whether there is a problem handing off files in the sandbox to some applications? I'm just not sufficiently familiar with the feature to know what complications might arise. Have you tried launching the image in another application, such as Paint?