The resolution of the playbackscreen ison my computer not very high.
When I am playing the clip with Windows Media Centre the the quality is must better then on the playbackscreen of Adobe.
When my movie is exported to a DVD the quality is also must better then on the playbackscreen of Adobe.
How can I improve the resolution of the playbackscreen.
As you've found, you can't really judge the quality of the video by how it looks in Premiere Elements. As long as you're using good source clips (especially from a miniDV camcorder) your results will be good.
1) Render often. Whenever you see a red line above your clips on your timeline, press Enter to render the timeline. This will give you a much clearer view of what you final output will look like.
2) Right-click on your Monitor panel and set magnification to 100% or below. Your video monitor has many times more resolution than your video, so it's always going to look lousy if you try to watch it full screen. Playing it at 100% magnification (which will take up less than 1/4 of your computer monitor) or less will ensure you're not looking at your video beyond its actual resolution.