Drop-out glitch with Fuji mini-DV tapes
Unfortunately, the outlook is grim. If you duped the tape and the dropouts still appear, the anomalies are regrettably on the master itself, or the DSR11 is malfunctioning.
To be sure, try the following:
View the master tape on a different deck, if possible. If glitches vanish, problem solved. Connect the AV/RCA out to the input on whatever digital deck you're using, and capture as usual with FCP. (If you need assistance with this step, I'll be happy to walk you through or send you in the right direction) Optimally, for a Hi8 tape, you would capture using DV 60i settings.
If glitches still appear, try capturing audio and video in two separate occurrences, I.E. One capture for video only, and a second capture for audio only. Sync in final cut.
If that doesn't work, your other option is to send the tape out to a post production house/lab, and see if they can do it - but if you've tried everything else and resorted to this option, the chances are slim that much can be done - Hi8 tapes are notoriously difficult to recover. Best of luck, and do let me know I can be of further assistance :)