We had difficulty downloading episodes from your feed Problem

This isn't a valid podcast feed. You have no 'enclosure' tags containing the URLs of your media files. Your 'description' tags (which iTunes does not read if the 'itunes:subtitle' tag is present) contain iframes, which they shouldn't, with links to media files. One is an archive.org URL beginning with https, which Blogger will not recognize as a media file for iTunes. Another is a YouTube URL - you cannot use YouTube videos in a podcast.

I can't advise on specifics with Blogger. However it should be able to produce a valid feed.

You must submit to it direct links to valid types of media files - .mp3, .mp4, .m4a, .mov, .m4v, not Flash, Windows Media, RealMedia or YouTube players. The link must begin with http not https, and must be a direct link to the file - your Archive.org link is to an embedded player and that won't work.

You will also run into trouble with your 'itunes:image' tag. This URL also is https and might work, though it should be http, but the image is only 585 x 585 px - it must be minimum 1400 x 1400px, maximum twice that, RGB, JPG or PNG and less than 500kB.

You are creating your feed in Blogger then submitting it to Feedburner to pass on to iTunes. Unless you have a specific reason for using Feedburner, such as tracking downloads (which can cause problems) it may be better to stick to the Blogger feed. You should be able to submit the image to Blogger though I can't advise how. Otherwise Feedburner has a 'Smartcast' feature which enables you to over-ride the equivalent tags in the original feed (on an individual basis) and you can submit the image there. If you submit it to Blogger check the result -some of these services reduce the image size, though I don't know whether Blogger does.

Archive.org should provide a direct link; if they offer a https one you may find it will still work with http. The test is to enter the URL in your browser's address bar; it should play directly in the centre of the browser window.

When you have amended your feed you should check it by subscribing manually in iTunes (from the 'File' menu). The top episode should download automatically and play when double-clicked. If that works the feed is probably OK to submit. If it doesn't then there's no point in submitting it until you've sorted the problem as each time you submit it and are rejected you will probably have to change the title slightly in order to be able to re-submit it.

That won't work, and I doubt you can extract it from the code. What is the URL of your Archive.org page for the file?

Some detective work threw up this as the URL for one of your files (with https changed to http)

http://ia601507.us.archive.org/29/items/TBPCE2/TBPCE2.mp3

You can get to the page for the file by clicking on the house icon at the right-hand end of the embeddded player:

In this case the page is https://archive.org/details/TBPCE2 - extract the URL from the 'VBR MP3' link in the column on the right, and remove the 's' from 'https'.

The 'Inaugural Episode' now works OK, so you need to do the same thing in the other episodes. The image is still the same, and the feed won't be accepted with it as it stands.