Q: Playing podcast, it jumps to next

Does this always happen on the same podcast episode?  Or is it on different episodes (not always the same) each time it happens?  If it happens with the same episode every time, the cause may be a corrupted audio file, especially since this is occurred before the current update.  Try deleting the current download and downloading the episode again.

Does the same thing happen when you stream songs or other audio content, such as iTunes U?

Does the problem occur with both video and audio podcasts, or just video?

Just trying to determine if the problem is specific to podcasts.  Or since you are streaming these podcasts, maybe it's related to the Internet connection, like the stream getting dropped after "caching" an initial portion of the podcast file.  So the podcast plays to a certain point, but then skips.  If it's related to the Internet connection, it's more likely to occur with other type of streamed media, not just with podcasts.  And it is also more likely to occur with video streams, because they use much more data (per second) compared to audio streams.

Are these audio podcasts or video podcasts?  Try going to the iTunes U section of the iTunes Store.  Those items are similar to podcasts.  Do you have problems streaming iTunes U items?