I am, among other things, a film professor (see http://www.film-prof.com). My students have to do a few papers that analyze some aspect of a film. Some choose to write about color, and I’m often treated to an analysis on pallets, palates, and palettes. Of course, only one of those is correct; the other two, to be fair, are amusing to visualize, and provide the occasional guffaw.
This is a palette:
It’s what painters use to hold their paints. It also refers to the range of colors in an image or film.
This, on the other hand, is a palate:
This is also referred to as the roof of your mouth.
And finally, this is a pallet:
A pallet can also be a straw mattress or a makeshift bed.
My students, of course, usually mean “palette” when they write, even when I’m reading “pallet” or “palate” or even an interesting variation of one of these three words.
The biggest thing to remember is that there are three words that sound exactly the same but mean very different things. And in the spirit of full disclosure, I confess that sometimes I have to look up the word to make sure I’m writing down the right one!