Well, it appears Apple has determined what the cause of this issue is and has repaired it, and I assume it was related to the encoding, because the reposted episodes are now playing fine without any change to the iPod. I had also been following the thread at:
http://discussions.apple.com/thread.jspa?threadID=1486046&tstart=0
and users posting there were getting replies from Apple saying the episodes were reposted to their accounts for download again, and they are reporting that they are now working on the 5G iPod. I can also attest to that; I replied back to Apple over the weekend referencing the other thread, and within two days they wrote back saying they had reposted the episodes, so I downloaded them, and they are now working on my 5G iPod. Plus I got a free credit for the one episode I paid for twice. The email response from Apple was as follows:
+Please accept my apologies for any inconveniences you have encountered with this issue. I have posted the episodes back to your account for redownload. Please follow these steps to download the episodes:+
+1) Make sure you're using the latest version of iTunes. It can be downloaded free of charge from the Apple website:+
+
http://www.apple.com/itunes/download+
+Note: Installing the latest version of iTunes will not affect your library or any items in your account that you haven't downloaded.+
+2) From the pull-down Store menu at the top, select Check for Purchases (if you're unable to upgrade and are using iTunes 6 or earlier, you'll find this option in the Advanced menu). If you can't find this option, you can also click this link to Check for Purchases:+
+
https://phobos.apple.com/WebObjects/MZFinance.woa/wa/checkForPurchases+
+3) Enter your account name and password, then click the Check button.+
+The episodes should begin downloading and appear in your Purchased playlist.+
+I have also issued a replacement video credit to your account "defurry", which you can use to buy the individual video of your choice from the iTunes Store. Please note, however, that video credits cannot be used to purchase or rent full-length movies or episodes of a TV Show that are listed as Season Only.+
+When you sign in to the iTunes Store with this account, the video credit will appear by your account name in the upper-right corner of the iTunes Store window. The next time you buy an individual video from the iTunes Store, the credit will be used to pay for the purchase.+
+I hope you continue to enjoy using iTunes and the iTunes Store. Have a nice day.+
So I am going to mark this thread that my question has been answered. My advice to anyone still dealing with this issue is to (1) report the problem via the link in your iTunes account order history screen, if you haven't already. (2) When you contact iTunes, reference one of these two threads (both threads reach the same conclusion).
I have always been a Mac lover, but like any relationship, difference of opinions occur, and for a while I was angry with them for trying to dodge responsibility for this. But it looks like we have made up, so we walk hand in hand off into the sunset. I trust they will do right by anyone else having this same problem, as the info presented in these two threads should convince the most obstinate customer service rep. Thanks Apple, and good luck, all.