Why am I using toothpicks as frets rather than metal frets or fret wire? Several reasons: toothpicks are easy to work with, readily available, are relatively straight and are easy to glue securely. Not to mention, they won't hurt too much if you leave a sharp edge.
I know that toothpicks aren't the ideal size for frets (they are too large) and have a tendency to "bend" the tone if you press the string all the way to the fretboard. I also have found that toothpicks absorb some of the sound.
I've been experimenting with wire frets. I couldn't use "real" fret wire because they mostly come with tangs (you can find fret wire without tangs, but that's just wire to me). Because the fretboard is plywood and thin, I was worried that the tangs wouldn't hold and would delaminate the plywood.
I have been using regular wire (I think its 16ga) that is normally used for gardening. I had to build a wire straighter (it was impossible to do this by hand/eye). And I am using normal titebond 2. Just make sure it dries really well before filing the edges. I also use a triangle file to make the slots more rounded (rather than square saw cuts).
So far, its been working fairly well, I'm still not sure which I prefer toothpicks or wire.
The two most important issue about frets are: spacing and material.
Fret spacing is based on a mathematical notion that when you double the frequency of a note, you go up an octave. Fret spacing needs to be fairly precise, or your instrument will be out of tune. Measuring is further complicated because fret placement is often calculated in decimal and translating decimal to 1/16" if difficult. My solution is to provide a pattern and mark the frets with a craft knife.
On most fretted instruments, you will find metal frets. Because metal does not absorb vibration easily, it allows a cleaner sound. You can purchase fret wire in all sorts of shapes and sizes, the big negative is that they almost always have a tang and need to be hammered into the fret board. Since I wanted a smaller lighter made from plywood, I needed a different solution. I considered gluing metal wire as frets, but about the only glue that stick metal to wood is epoxy....and epoxy is messy and smelly. I chose toothpicks because I know normal wood glue will easily hold toothpicks in place. Yes, they are a little higher than metal frets, but it means you don't need to press as hard.
Frets are used to change the pitch of a string when playing.