You can play the file that is output by raspivid in mplayer. You can also try on another computer using VLC.
All you doing with ffmpeg is copying the data stream from the source to destination. You can simply this by renaming the extension from .h264 to .mp4, but you may as well amend raspivid extension to use .mp4
Extensions todo not govern what data lies in the file. If the stream is h264h264
that is what it will be regardless of the filename or extension.
The doubling up in speed might be caused by the -r 24
option on ffmpeg. If you do not need to change source settings then there is no need to specify this option. It may be the culprit.
Just play the original video0001.h264
file and see if that is what you were epxecting.