I shoot with an XL2 and import onto FCP, with the scratch disk being an eSATA Hard Drive. When I send it directly to the hard drive it drops a frame about every ten minutes and stops importing. If I go directly to the internal hard drive, it does not have this problem.

Can I set FCP to send the data to the Hard Drive and to ignore dropped frames? Also, will this affect the video quality significantly?

There is an option to ignore dropped frames while importing. Go to Final Cut Pro > User Preferences... In the General tab there is a check box that says "Abort capture on dropped frames." I'm not sure what this would do to the captures video though. I have never heard that capturing to an external drive would cause problems. You might want to check the speed of the drive, if it's too slow maybe it can't write the video fast enough.

Are you capturing footage? If that's what you mean by importing, then you don't want to allow dropped frames. Or your final edit will have missing frames and look jerky.
People used to have this problem because of a glitch with spotlight, you can search for that in this forum.

The hard drive is a LaCie 500BG one with eSATA but that's not the problem cause I had a WD FireWire 400 drive before that and it had the same issue. This has been like this in FCS 1&2 regardless of what camera (XL2 or Xi). I also believe it happened on my old iMac G5 as well.

Yeah, that sounds like a Spotlight problem. Go download Spotless and disable Spotlight on your external drive.