Your camcorder is what's called a "hybrid" and can shoot in a variety of standard definition modes and quality levels. It's hard to advise you without knowing some specifics.
What mode are you shooting in? If you're going to edit your video in Premiere Elements, you will need to shoot in HQ mode.
When you set up your Premiere Elements project, which project settings did you use? You must use the Hard Disk/Flash Memory Camcorder/Standard Definition project preset for this type of camcorder.
How did you get the video from your camcorder to your computer? In version 7, you should be attaching the camcorder to your comptuer via USB and then using Premiere Elements Media Downloader (under the Organize tab, go to Get Media/From AVCHD or Other Hard Disk Camcorder) to import the video into your project.
Although, by nature, your computer will emphasize your camcorder's interlacing (which appear as horizontal lines) and these will not be issues when you play your video on your TV, there are certainly video issues that are unavoidable. As all videographers know, you should never shoot video of a person wearing a pin-striped shirt or a person standing in front of venetian blinds. Narrow lines produce a distortion called a moire -- and, if this is what you're seeing, there's not a lot that can be done about that except avoid shooting it, unfortunately.
I belive thats what I'm seeing. I do download the camcorder and use the settings you suggest in Premier Elements 7. I am switching the camcorder setting to HQ. I was shooting in standard mode.
Thanks for your help and I'll try to stay away from those narrow lines.