Other than spending some money and getting a faster computer (I wish I had this option 
), there really isn't any way to speed things up here. Some people have noted that the client loads a little quicker after the first time, but it's not really something I've noticed myself. I never thought about load times with/without the map either, so that also might save a little time.
Defragging the hard drive can help a little, too.
My demo launcher can take up some memory. If you're short on memory and you're just doing the demo with no options anyway, simply make a shortcut to CityOfHeroes.exe and drag your demo to the shortcut. That keeps my program out of your memory space.
The console has the demoplay command but I've never been able to get the command to work when playing a demo back. Or even just reload the demo currently playing. That would be mighty sweet if it could.
AH HA!!! Here's a way I just discovered if you've got a lot of memory...
Start a demo playback of some smallish demo. Be sure to tell the game NOT to hide text so you can see chat bubbles and, more importantly, the console. Hit the ~ key to bring the console down. Give the command 'demofps 9' and all the action will stop. Alt-tab out and forget about the demo completely.
As long as that demo is sitting there in memory, further demos you launch will load faster. Not a ton faster, but faster.
(The DemoFPS command is supposed to be used from the command line to launch demos at faster or slower speed. It would be nice if this worked from the console so we could speed up or slow down motion while the demo played but it's actually broken and causes the demo to go into some weird empty state. That's sure handy for this purpose, though, as it leaves a lot of game files in memory while not taking up a lot of CPU. With those game files already loaded, the second instance of the game can load a bit faster.)
While editing demos I have to wait for the CoH client to load every time I want to view a fix. Is there a way to speed up this process? Is it faster when I remove the map first?
Currently, I"ve been trying to edit one clip while the other is loading and running, but eventually I'll have to view the whole movie over and over and over.