I tried writing different output formats, with "copy" for both video and audio.
Input is a 1920x1080p AVCHD file with 23.976 frames per second.
In the "File"/"Information" window, avidemux says the files frame rate was 47.952 (which is twice the real one)

. Replay and editing works fine - using the correct frame rate.
When I use "Save" to write using the "MP4v2" muxer, the resulting file has the correct frame rate according to "mplayer":
VIDEO: [H264] 1920x1080 24bpp 23.976 fps 90469.6 kbps (11043.7 kbyte/s)
When I open the .mp4 file avidemux wrote again with avidemux, it displays an odd frame rate in the "File"/"Information" window: 24.750 fps.

When I use "Save" to write using the "Mkv" muxer, the resulting file has a slightly odd frame rate - according to "mplayer":
VIDEO: [H264] 1920x1080 0bpp 23.917 fps 0.0 kbps ( 0.0 kbyte/s)
When I open the .mkv file avidemux wrote again with avidemux, it displays 47.952 fps in the "File"/"Information" window.
Very strange... now I wonder whether all these tools are just making wild guesses on the frame rate, or where all these inconsistencies come from. I guess I need to write and replay really big files to find out whether these odd values will cause actual trouble (in terms of de-synchronization, playback stutter and such).