Inspecting files
You can use the ffprobe command to gather useful information about a video file:
ffprobe -show_format -show_streams big_buck_bunny.mkv
This can be useful for example, when filing bug reports, or discussing in chat.
Remuxing files
Another good test, is to see if remuxing the file into a new video file helps:
ffmpeg -i big_buck_bunny.mkv -c:v copy -c:a copy remuxed_file.mkv
If you are asked for a sample of a video (e.g. for developers to analyse), you can use
ffmpeg -ss 120 -i big_buck_bunny.mkv -t 30 -c:v copy -c:a copy 30_second_sample.mkv
The above command starts at the 120-second marker, and takes a 30-second sample of the video file.