SOLVED!

Here you can find a simple patch for the Joomla 3 (not K2!) bug that causes this unintentional opening of the calendar (the bug is still present in Joomla 3.1.5)

creativeprogramming.it/en/knowshare/item/48-joomla3-js-calendar-issue-unwanted-popup-enter-fixed

It was due to a wrong handling of javascript keypress events, so any time you hit enter in an inputbox the first available calendar opens.