Thank you very much, Plotinus. I think I have developed a sort of Helper for this problem.
If you use IrfanView, note that it regularly messes with the palette and color depth when you copy and paste new unit icons to your units_32.pcx sheet. Because of this, you will sometimes see weird graphics in the Map Editor and the game (like a magenta square behind the unit icon).
Here is what one programming illiterate (me) did to solve this problem, thanks to the help of the CivFanatics forums.
First, make sure that the units_32.pcx sheet you are going to use has a palette that is correct. You can test this by opening up the Map Editor. if the units look good on the map, then you are okay.
It is a good idea to save a back_up of your units_32.pcx file just in case you mess something up and cannot fix it. I usually save my back-up as backup_units_32.pcx
Next open your units_32.pcx sheet in Irfan View. Go to Palette\Export Palette and save it to your Units directory (just so it is close by).
Next, copy and paste the units that you want to add to your units_32.pcx sheet. In doing so, IrfanView just jacked with your palette! (You can see this when you open your Map Editor if you save the units_32.pcx sheet as is.)
Next, when you have finished properly adding your unit icons to the sheet in IrfanView, go to Image\Decrease Color Depth and change it to "256 colors (8 BPP)." (If it is already 256 colors, you don't need to do anything, obviously.)
Next, go to Image\Palette\Import Palette and import the Palette file that you saved.
Next, save the units_32.pcx sheet. Voila! No more magenta (or other color) square in the background.
I admit that this is an overly simplified procedure, but I have no clue how to edit palettes or anything else, let alone keep IrfanView from jacking with the palettes! I am just a copy and paste guy. If you need help with any other part of adding units to your mod, make sure to check out the forums here at CivFantatics - they are excellent. This little diddy was designed for people like me who are using the free IrfanView program, who also know nothing about anything else. Take care.