It sounds like the files are becoming corrupted, however there are any number of possibilities how this could be occurring. If you are shooting RAW, it is possible that the preview jpeg (used for on screen display on camera and thumbnails on a PC) are actually intact, but the much larger raw data portion of the file gets corrupted. If shooting JPEG, there are slightly fewer possibilities since the on camera preview would indicate the file was intact on the camera, but many of the possible problems are the same.
At some point along the file's path it is getting corrupted. It could be a problem with the camera itself causing the file to never be fully written, it could be a problem with the memory card that results in the storage failing, it could be a problem with the memory card reader failing to read the file entirely or without error, and it could be a problem with the USB port or software opening the file on the PC that could be resulting in data loss or false indication of an error.
The best way to trouble shoot this kind of thing is to start replacing factors from that list, one or more at a time and see if you can get the problem to stop. Try connecting the camera direct instead of using a card reader, or use a difference card reader, use the same card in a different camera and see if it gets corruption, use a different card in the same camera and see if you get the problem, try switching between RAW and JPEG, see if that makes a difference, try installing another piece of software to look at your images and see if that works. Try accessing them on another computer altogether.
Based on the results of those kinds of tests, you should be able to narrow down what the problem is and what needs to be done to fix it.