Hope this story of trouble-shooting this problem helps someone in the future.
For some strange reason, when I listened to a podcast using the Music app through the Apple earphones with remote on my iPhone 4, the right side has no sound. However, when I pull the earphone plug out one notch, I get sound from both sides, but the remote controls no longer work. At that point, I was sure I had a hardware problem, but where it lay-- earphones or iPhone 4, I didn't know.
1. For my first step, I tried the earphones with another iPhone 4, and got the exact same results. That convinced me that it was a problem with the earphones, but then I tried them on our iPad and they worked fine!
2. That ruled out the earphones and got me wondering if both iPhone 4's earphone jacks were flakey or misbehaving. I had read about the old fuzz in the jack problem, so I used an air blower to clean it out, but it made no difference. I still figured that maybe both jacks were stressed in some way, although two of them?
3. Then I read that some people found different apps worked--and even specifically that running Skype could solve things. That didn't work. However, it led me to try various streaming apps (e.g., Portal to the Universe, NPR) and everything was fine-- sound from both sides and remote controls fully functional.
At that point, I was convinced there was something odd going on with the Music app.
4. Finally, it occurred to me to try other podcasts-- and even other episodes of the particular podcast. They all worked fine.
So, it ended up being one particular podcast-- and, while I still do not know why, it means that the earphones, the headphone jack, the iPhones are all in fine shape! Yay!
In any event, the bottom-line is that it's really smart to consider *all* the variables that could be affecting the situation--especially the most obvious ones that you wouldn't even think about it. As it turned out, in my case, I had tested the very same podcast on both iPhones, so no wonder I got the very same results!