I have a DCT 3416 1, firmware 16.35 connected to a Samsung HT-TQ85 home theater A/V receiver via HDMI. Output of A/V receiver is connected to Samsung S5053 Plasma via HDMI out. Before 16.35 I was not able to do this and got the Green Screen issue.
I had to use component cables to get around the problem. When I turn on all three, the TV screen says waiting for signal until the A/V receiver comes on and the picture and sound come on. The sound comes from the A/V receiver. Everything is fine for about 3 seconds and the Green screen flashes on for about a second and the video and audio go way out of sync with the audio lagging the video. Sometimes when switching channels from an HD channel to a non-HD channel the green screen flashes and the video and audio goes out of sync. It has even happened while just watching a channel or a recording.

There are two ways to get them back in sync, one is to turn the HDMI Audio on which sends the audio to the TV and turn it off again. This syncs everything up again until the next green screen. Second, change to another HD channel and back again.

Not sure which component is causing the problem. Has anyone else had this problem?

HDMI switching has been problematic for many devices since day one. How about this? DCT 3416's HDMI signal directly to your Samsung plasma and take the digital sound out of the plasma to an un-used input on your sound system? I think the sync issues will be solved if you do this.