The top portion of the Harken Furler on my catalina 22 sailboat turns
along with the sail as it unfurls, causing the jib halyard to wrap
around the jib stay.  The furler top has two parts - one is supposed
to stay stationary and is connected to the jib halyard; the other is
connected to the jib and rotates as the sail is furled.  There is no
apparent way to tighten the top portion of the furler to prevent it
from moving.  What's wrong?

Have you seen this?  Unfortunately, only the cached site opens:
http://64.233.183.104/search?q=cache:Er-gdpsXKkgJ:www.harken.com/furling/furlserv.php+harken+furler&hl=en&ct=clnk&cd=1

Search with:   harken furler
to find it, if the string doesn't work.  The site title is:
Harken: servicing a harken furler

From the warning about dirt or grease on the bearings, this seems to
be something that could increase the torgue on the top connection.

Good luck and fair sailing!