There are sockets on the right side for a Speaker-Mic. They're covered with a rubber flap. The rubber flap is help in place with a Phillips head screw that looks like it could be easily removed (not confirmed) if you wanted to use a Speaker-Mic most of the time.
The tempting (standard size) 1/8-inch socket is for the microphone, not for your Walkman headphones. The speaker would plug into the slightly-smaller socket. Sorry. It's intended for Speaker-Mics, not your stereo Walkman headphones. But some Speaker-Mics have standard 1/8-inch headphone sockets...
Deal Extreme sells a Speaker-Mic (Referral) for under $10, but I've not yet bought it and tried it to see if it'll work with this radio. It probably does, but I've not confirmed it yet.
[See later post above.]