Could not complete your request because of a problem with the file-format module interface.
A file could not be opened because it was not found or of an unknown format.
The most common cause are broken or screwy system level file associations and protocol handlers that tell your computer which programs to use to actually open a file when you use a double-click, drag & drop or other system methods to invoke a file operation. Since this is not controlled by anyone, it can happen that multiple programs register the same file extension like for instance *.psd. That can mean that the file opens in a different image viewer or editing program and not in Photoshop if it is actually a PhotoShop Document. On the other hand it may not open at all if someone simply used the same extension for his file format, but it actually means Popular Survey Data or similar. Naturally then it will not contain any image data and Photoshop can’t work with it. This applies even more so to auxiliary file types like the ones used to save brushes, actions and swatches that may never correctly import by just double-clicking on them.
Related to the previous, files may not be possible to open when those handlers are blocked by security tools or the hand-off chain from the double-click registered by your operating system to the actual opening of the file is interrupted otherwise. This can include hardware problems like fragmented drives, bad connections to external storage devices and interruptions in network connections just as well. Sometimes they are genuine issues with cables or connections, sometimes performance issues because a disk is already being used a lot. Also time-outs from drives that have gone to sleep needing to spin up or network connections being too slow can cause Photoshop to simply give up on opening the file.
Another critical issue is of course missing or messed up file parser plug-ins. There is basically two standard scenarios here: The user has copied his beloved filter plug-ins from an older version of Photoshop to a newer one and inadvertently also copied incompatible or redundant file format plug-ins or in the other case uses an incompatible third-party plug-in e.g. for creating icons.
Finally, a very specialized case that is sort of a combination of all the above points are Smart Objects and Smart Filters that attempt to use dynamic data directly from the source of a placed file. Handling Raw files from your camera via Lightroom and/ or Adobe Camera Raw would be one such example, but this may also affect Illustrator files or other types. When going from one program to the other, communication could be blocked or due to differences in versions, which even could have been caused by a failed update of one of the programs, the file format is not understood.
Resolution or workaround:
To begin with, most issues can be rectified by just reinstalling the program. This will reinstate default file associations, place compatible versions of the plug-ins and give you a chance to straighten out potential hardware issues beforehand and optimize your set-up by e.g. choosing a different install location. To avoid remnants and invalid configuration data of the previous install to be left in place and get in the way, it is necessary to try and uninstall the program using the uninstallers and clean out any folders. You may also need to run the Creative Cloud/ Creative Suite Cleaner Tool as explained here.
If you are reasonably versed in computer stuff and know your way around, you can also try to manually fix file associations and all that stuff. This is explained on this page. Some guidance on straightening out potential hardware and performance problems is provided on this page. Of particular not should be fitting up your drives by defragmenting and reorganizing file structures as well as making sure that things like USB connections actually work reliably without dropping out or the external drive going into idle modes prematurely. When you use double-clicks or drag & drop, try to open the files using the relevant menu functions instead and see if it makes a difference.
When using specific plug-ins, obtain the correct version from the vendor/ supplier and do not use outdated ones. It may cost a few bucks to upgrade your plug-in suites, but it can save you a lot of trouble. Similarly, if you use plug-ins across multiple programs, make sure you have the same version. This explicitly also includes verifying the update status of Camera Raw and your Adobe programs in general. Even things like unwittingly installing the latest Adobe Reader and it introducing new file versions of the shared PDF libraries that then could prevent you from opening those files in your older version of Photoshop need to be considered. Going back to an older version to undo the damage may then be your only option.