Hello agentmitten,
Here are the concepts behind MIDI and other files which might help you understand why MediaEditor cannot edit MIDI files.
Think of MIDI as sheet music for computers as opposed to "recorded sound". This is why a midi file is generally so small. It contains four pieces of information for each note played: a) the pitch, b) the instrument, c) the volume, and d) any effect that should be applied. Some formats also allow for lyrics and other things to be included.
You sound card has a device on it called a "Wave Table" which is basically the "sound" that the relevant instrument makes when it is played. The MIDI instructions (play a trumpet, middle C for .25seconds) are sent to the sound card and are converted to audible sounds only at that stage.
This is the main reason that MIDI files sound so artificial. The wave tables generally include only a few different pitches and everything else is generated based on the profile of those wave samples that it does have.
:-/ It's like trying to edit the recording when you've only got the sheet music. It is possible, but you've got to make the recording first.
There are several MIDI-to-wave converters available (try searching Google). You can then use MediaEditor to edit the wave recording.
If you REALLY want to edit the MIDI file, software is available, but it is a little more complex (usually) that Media Editor. You can search for programs like "Sibelius" and "Cakewalk" just to name two -- there are probably a thousand simpler ones that can get the job done.
Sound cards coming out now are fitted with some really impressive wave tables. I owned a Creative Labs AWE 64 (way back when) which was on of the first cards to bring "decent" (a relative term!) sound to MIDI. Things have improved since then too.
I hope this helps!
P.