In reading through the responses here, although they were very helpful I thought I'd detail how I manage podcasts on my iPhone as this is what would help me. As the whole iTunes paradigm of 'syncing' is very non-intuitive from my perspective as opposed to simply selecting and deleting, or dragging and dropping, I've endlessly been frustrated in trying to deal with it.
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Step-by-step:
I connect my iPhone to my iMac and open iTunes.
Under DEVICES in the left sidebar, I select the iPhone icon.
In the main window, I go to the top center navigation and select the Podcasts button (position 8 from the left in the horizontal listing).
Under the navigation in the main window below the navigation I select the 'Sync Podcasts' checkbox in the top left.
In the left column of the main window, titled Podcasts, I select the Podcast I want to manage.
The episodes I have in iTunes show in the right column, each episode having a selectable checkbox.
I check the ones I want on my iPhone and deselect the ones I do not want on it.
At the bottom I select the 'Sync' button on the right.
This adds the newly checked podcasts to the iPhone, deletes the ones that are on the iPhone but that I've unchecked in the right column in iTunes, and leaves the ones on the iPhone that were checked and unchanged in iTunes. When I return the next time, the state of the checkboxes reliably represents which episodes are on the iPhone and which are not.
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The conceptual problem I have is that one can only really interact with attached devices (iPhone, iPod, iPad) through iTunes on a computer, not interact with the device directly. Now that apparently you can delete an podcast directly on an iPhone, it can add confusion as iTunes only recognizes that the podcast is missing, not that it necessarily has been deleted as it is still listed in iTunes' representation of the state of podcasts on the attached device.
HTH.