The first figure is the mail away Agent Faces figure. For this figure, the head was a either a new sculpt based off of the '92 Duke or a slightly modified version of that head. The production figure's facial hair was just a paint application. In the sample below, though, this application was missed. The result is a very different looking figure. While the sample is production level, it's more likely a case of factory error or poor quality control than an actual variant. But, it's interesting nonetheless.
The second figure is the pre-production 2002 BJ's Dial Tone. This mold was released with no mustache in 2000, but the production figure in 2002 did have the mustache. This pre-production figure has differences other than the facial hair, like the differently colored elbows and general difference in the green arms. But, the mustache is the most glaring difference.
The final figure is, again, likely a factor error rather than a variant. But, it is a 2003 Python Patrol Major Bludd figure with no facial hair. Bludd is very odd without his trademark mustache. So, this figure is boldly different from any other appearance of this head. While it's likely not a variant, it does offer further proof that factory goofs can make their way to retail.
Click on the Rarities tag to see more oddball items. And, Rarities Month II will be coming in June of 2017.