What are the physical dimensions of the psd file? FCP doesn't care about dpi (in video space dpi is largely irrelevant). All that matters is the actual size of the file (1280x720, 1920x1080, etc.). Make your psd file the size you need for your timeline (or bigger if you plan on scaling into it using the Motion tab).
If you have a 300 dpi file that is 320x180, all FCP sees is 320x180. Drop that in a 720 or 1080 timeline and it'll look bad.
Ryan Holmes
http://www.ryanholmes.me
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