The key phrase here is on the second page of the letter and which reads:
While Apple of course has no general objection to proper use of the descriptive term ‘podcast’ as part of a trademark for goods and services offered in the podcast field, it cannot allow marks that go beyond this legitimate use and infringe on Apple’s rights in POD and IPOD.
So after all that fuss, it seems Apple is not out to stop us all from using the term "podcast" after all. On the other hand, there are good reasons to rather change to a new term. As Leo Laporte put it in his post on this topic:
Truth is, I’ve never liked the word podcast. It causes confusion. In the past couple of days two people have told me that they can’t listen to my shows because they "don’t own an iPod." I have to explain constantly that podcasts can be listened to on computers, phones, MP3 players, and CDs, as well as iPods, but because of the name the confusion persists.
The question is whether the term "podcast" has become so entrenched that there is little likelihood of every converting people across to a new term. I see that Leo has stopped referring to his audio shows as podcasts and now refers to "Netcasts you love from people you trust". For my part, I am going to happily go back to calling these podcasts, well, podcasts.