Repair corrupted video files
Completely depends on the video codec and container format, there is no general tool to fix corrupted video files.
Regarding avis with missing headers there is a good answer on this question.

The info there also helps with recovering other video formats.

To find more info about a certain file I recommend using MediaInfo in addition to ffprobe. It offers some more info about codecs and container properties than ffprobe and is easier to read.

If chunks in the video stream are corrupt it won't hinder playback of the stream you will just experience artifacts around these chunks.