There are probably GUIs that allow you to make clips from MP4 files, but I still do it the old fashioned way using the mp4box command line (Windows). Maybe when I get more free time, I'll add some screenshots to this post, but for now, just read along.
It's really not so hard once you learn the little quirks.
You can grab mp4box here (or just google: mp4box download)
http://www.videohelp.com/tools/mp4box
Play the .mp4 file and find the approx. start and end times for the clip you wish to make. Convert these times into the total number of seconds from the beginning of the movie, e.g. if the start time is 01:01:01 (one hour, one minute, one second), then the elapsed time in seconds in 3600 + 60 + 1 = 3661 sec.
Put mp4box inside the folder/directory where your .mp4 file is located. Open a command window (hold down SHIFT key and right click inside this folder, and select "Open command window here"). Type the following in the command window:
mp4box filename.mp4 -split-chunk S:E
where filename.mp4 is the file name of your .mp4 file, S = start time in seconds, E = end time in seconds
For example:
mp4box 69thStVice.mp4 -split-chunk 3661:3961
(for a five-minute clip beginning at 01:01:01; 300 sec. = 5 min.)
Then hit the Enter/Return key.
If your file name has any spaces, then you'll need to put the file name inside quotation marks, e.g.
mp4box "69th Street Vice.mp4" -split-chunk 3661:3961
In the above example, your new file will be automatically named:
69th Street Vice_3661_3961.mp4
You may get up to ten seconds of additional footage at the beginning of the clip, depending on where the key frames fall in relation to your preferred start time. If you don't want the extra footage in your clip, then you'll need to re-encode the vid and ensure that there is a keyframe at the beginning of the clip you want. When I get some time, I'll add to the tutorial and explain how to do that.