So, all my products are showing in front end at their sale prices. In the back end there are saved start and end dates in the product/prices screen. Clearing the start and end dates for the special prices of individual products does not work: upon save either the from date or both from and to dates are filled again. If the from date is filled, it is today's date, if the to date is filled, often it is ten years in the future. I can set the from date to a future date and that saves OK. I hear I should not be using phpmyadmin to edit tables directly so I hope there is another, safe method. Helps!
Why not set a date in the past for both? That's standard behaviour for Magento to set the from date to today when saving a special price. Just set the Special Price To Date to a date in the past.
You can also do a mass product update. Select all products and on the top right choose "Change attributes" then you can edit the special from/to date for many products at once. (make sure to tick the Change box)