Well 473nm was used for initial mixing for RGB laser shows as blue diodes didn't exist back then, and argons (457nm specifically) were difficult to produce and (488nm argon) was not suitable for mixing. Plus a lot less heat is generated. 473nm is described as a powder blue, and it's uncommon in pointers as it's not easy to produce.
589nm... that there is a mystery to WHY it was produced in a Nd:YAG at all. I know scientists are looking for a more effective way of producing 589nm (for astronomy purposes, feel free to google that) than a sodium vapor laser, however why SFG was their choice is beyond me. It's rather inefficient, not to mention extremely hard to produce... You may want to mention this wavelength's precursor, 593.5nm. There's no purpose other than the purpose of it being easier to produce than some of the other wavelengths Nd:YAG can be forced to produce (while not being easy at all to produce itself). Really it's only there to fill some of the gap between green and red.
1064nm is pumped into a frequency doubler to produce 532nm (as frequency doubling is wavelength-halfing). It's also used in some cutting tools where deep IR from CO2 lasers aren't suitable. But mostly frequency doubling for 532nm.
With 532nm... how many people in your chemistry class know what a dye laser is?
You may want to explain to them that their green pointers they buy at the beach are made from this process.
I don't go into the UV wavelengths in my research so I can't really say much on their behalf.
Hopefully some of what I provided is useful,
-Zach