Transmission Shifting Slow?

Every so often you notice it: The transmission shifts a little late, or maybe it seems to miss a gear entirely. Then it’s okay again… for a little while. Worst of all, there’s no rhyme or reason behind the condition. One minute it’s fine, the next it’s not. So you pop the hood to check the transmission fluid level. Then you notice it: A big mountain of corrosion on the battery terminals. You’ll have to take care of that, but it can’t have anything to do with the transmission, right?