By default Final Cut is set to play videos back in a way that’s optimised for performance rather than quality. For those of us working on potatoes that means some seriously blurry play back. To get your video to not look like you’re watching it through a steamy window do the following:
Click the View As dropdown in the top right of the video window.
Under the Quality section choose Better Quality.
Voila! Hit play and everything should be looking much better. Changing this setting is going to make your computer have to work harder so it could be worth waiting for your clips to render before playing them.