You might get a more definitive answer over on the Hot peppers forum here where all the dedicated pepper growers hang out. To me it looks like a disease called Bacterial Spot but I'd double check with the growers there before buying that opinion.

I'd also ask them about the size of your container because 2 gallons is much smaller than is usually recommended as a minimum size for pepper plants based on what I have read. Reason I question it is that the edges fo the leaves look darkened and stiff and that is often a sign of a rootbound plant.

Dave

Here is a link that might be useful: Hot Peppers forum

Thank you, digdirt. I'll move over there.