So, like many users, I use my phone to play the podcasts (Samsung S3 Galaxy mini, on android). I put it in the "key pocket" that is in the back of my waistband, and run my headphones under my clothes and out the top to my ears.
This morning I forgot to disable an alarm before I started, so half way round it went off. I didn't want to stop or unhook myself, so I swatted at my pocket until the alarm stopped. When I got home I discovered I'd deleted my home screen wallpaper! I guess the real answer is going to be one of those smartphone armbands.
I've also finally got to grips with mapmyrun. It confirms what I already suspected - I don't jog any faster than I walk. This is partly because I'm being extra careful with my knees on the running bits, and conversely pushing myself to walk very briskly on the walking bits. Maybe things will change as I go on. In week 2 I'm doing 3km in my half hour...