Whatheck,
Thank you! Using Image Capture helped me to figure out the problem. Good idea, Whatheck.
I figured out the problem. A couple weeks ago, I decided to change the time/date format from Gregorian MM/DD/YY to Taiwan's YY.MM.DD, where the first year was 1911 (the foundation of the Republic of China--not to be confused with the Communist "People's Republic", which is China and not Taiwan). So, this is year 99 of the ROC. Videos taken with the calendar set to ROC had MM/DD/0099-like timestamps. All I did was switch back the calendar setting from "Republic of China" to "Gregorian", make a test video, and then plug in the phone. All videos taken during the time the phone was set to ROC were imported AGAIN and re-split. Now everything is fine. (Except the original 2005-stamped imports are still there, taking up a little disk space. If I ever have way too little disk space and way too much time, they can easily be removed. Haha.)
I originally preferred to see ROC dates in iCal. Now that I know it messes up videos, I can live with Gregorian dates. I still don't know why only videos were affected by the calendar selection.
Thanks again, Whatheck.
Ray