So the salt bridge allows diffusion of ions to maintain charge neutrality of half cells in an electrochemical cell, permitting current to continue.  So when a battery is not in use, the diffusion can continue.  Now, this is the diffusion of the electroyte solution in the salt bridge itself, not the actual ions involved in the reduction and oxidation, correct?  In my notes I have:

"When a battery is not in use, the diffusion can continue through at a slower rate.  In this case, Fe²⁺ can "diffuse" to Zn-Zn²⁺ half cell and be reduced.  Eventually most Fe²⁺ are reduced and battery is no good (dead)."

How is it that the Fe²⁺ can diffuse across the salt bridge?  The reason I have diffuse in quotations is because there is a missing word in my note here and I assumed this is the word that fits in--maybe it wasn't the word though.

Fe2+ can still diffuse over. All things tend toward equilibrium, so if their is a high concentration of Fe2+ somewhere and also a low concentration someplace else, and there is a means for the ions to travel, they will.

So does this only happen when the battery is not in use?  I was always under the impression only the ions present in the salt birdge were the ones doing the diffusion.

So does this only happen when the battery is not in use?

I would think this would happen when the battery was in use.

I was always under the impression only the ions present in the salt birdge were the ones doing the diffusion.

Usually, but there is nothing stopping the ions being formed in solution at the half cells from diffusing as well.