I usually don't use the Download MP3 button on the Podcast page, but I wanted to listen to the podcast today without much effort. I tried to get it to work either by just clicking on it or by right-clicking on it and choosing "Save link as...", but had no luck. I tried this on a bunch of the podcasts and came up empty.
I am running Win 7 64bit - Google Chrome Version 30.0.1599.101 m
I also tried it using Internet Explorer and the latest Firefox with the same results.