Does the associated extension matter when outputting savefiles? Could I use just any old one- to three-letter extension I felt like using (save from obvious problems that may occur, like using .dll or .exe)?
No, it doesn't matter. Yes, you can use any valid extension. Yes, you should probably avoid important extensions like exe and dll. =)
In response to Crispy
But, if you use something like dll, people probably wont want to play with it for fear of screwing something up. I could easyly be wrong though. Trying to scramble the names and putting an odd or common file extentions might be a good way to keep people away from playing with their save files if they host(but if they host, they have the right to do whatever they want with those files short of copyright infringment)