So I have all the components to build a generic Arduino clone, with the exception of a proper 16MHz crystal. I have a number of others, but I wouldn't be able to get a 16MHz crystal for a few weeks. So, I'm wondering what I would have to change in the bootloader and in the other code in order for this to work.
Too much effort to get all the libraries etc working for other crystal speeds.
Just burn the lilypad bootloader. It is designed to use the internal clock set to 8Mhz.
You then need to choose the "Lilypad" board when uploading sketches too.
When you get your crystal you can burn the decemilia bootloader to take advantage of the faster speed.
Note that this applies only is you are using an AtMega168, not a Mega 8 or mega328.
It's not really that hard to find a 16MHz crystal:
Alternately you can use a three-pin ceramic resonator and eliminate the extra capacitors needed with the crystal: