There are some options for a better compatibility:
ffmpeg -i broken.mp4 -c:v libx264 -profile:v baseline -level 3.0 -pix_fmt yuv420p working.mp4
With -profile:v baseline -level 3.0 you make the file more compatible with most older players, including WhatsApp ;). Although, this disables some advanced features.
-pix_fmt yuv420p is necessary to compile to baseline (YUV planar color space with 4:2:0 chroma subsampling).
Also, you can adjust other options as bitrate, framerate, audio, etc.
Source: H.264 docs