Assuming the MP4 clips have all the same settings (frame size, bit rate, etc) and use h264 video and AAC audio, this can be done on the command line with ffmpeg.
The easy, but less efficient way to do it:
ffmpeg -i input0.mp4 -c copy -bsf h264_mp4toannexb temp0.ts
ffmpeg -i input1.mp4 -c copy -bsf h264_mp4toannexb temp1.ts
ffmpeg -i "concat:temp0.ts|temp1.ts" -c copy -absf aac_adtstoasc output.mp4
The slightly more complicated way, that doesn't require intermediate files to be created:
mkfifo temp1 temp2
ffmpeg -i input1.mp4 -c copy -bsf h264_mp4toannexb -f mpegts temp1 2> /dev/null & \
ffmpeg -i input2.mp4 -c copy -bsf h264_mp4toannexb -f mpegts temp2 2> /dev/null & \
ffmpeg -f mpegts -i "concat:temp1|temp2" -c copy -absf aac_asdstoacs output.mp4
Either of these will be completely lossless.
I notice that you've solved your FCP-specific problem by using the correct settings, per that comment...
It would help if you told us what resolution (in pixels) the clips have and how long they are. Otherwise this question cannot be reasonably answered. The first sample clip has 0 bytes, by the way. Also, since I don't have FCP, could you show us what options there are for rendering the final video? Finally, do you have to use FCP for this? – slhck – 2012-12-09T11:23:12.183