Ipod nano touch podcast sync issues (can't delete some podcasts) As you can see in the photo, my iPod has several podcasts.  But iTunes only displays one.
It doesn't always show the subscribed podcasts, sometimes does, but not always. If I drag (copy) a podcast to the ipod, it then shows on iTunes, but it may dissapear later.
In the iPod, the podcasts always show, but I can't delete the ones I don't need anymore.

How can I solve this?
Should I manage all podcasts through subscription and not drag individual episodes? or can I mix both methods?
The podcasts part of iTunes just manage those you have either subscribed to, or subscribed and unsubscribed but still have episodes. It looks like your issue is related to trying to manually manage these, which will let you add the files to your iPod, but iTunes really doesn't know about the structure behind them. 

I would recommend having it manage them for you. In that case, you can also tell it to delete those (or keep those) you want after you listen. 

For example, I have a couple of concerts from NPR on my iPod that I keep, but my other daily/weekly podcasts delete after they have been listened too. 

I expect the reason you are seeing the difference between iTunes and the iPod is the way you are currently mixing the two methods.