En wp-includes/template-functions-general.php:

~línea 457: Cambiar $pad = intval(date('w', $unixmonth)); por $pad = intval(date('w', $unixmonth-1));

~línea 478: Cambiar if (6 == date('w', mktime(0, 0 , 0, $thismonth, $day, $thisyear))) por if (0 == date('w', mktime(0, 0 , 0, $thismonth, $day, $thisyear)))

En wp-includes/locale.php:

Ordenar correctamente los días de la semana:

$weekday[0] = __('Monday');
$weekday[1] = __('Tuesday');
$weekday[2] = __('Wednesday');
$weekday[3] = __('Thursday');
$weekday[4] = __('Friday');
$weekday[5] = __('Saturday');
$weekday[6] = __('Sunday');

y cambiar

$weekday_initial[__('Sunday')]    = __('S');
$weekday_initial[__('Monday')]    = __('M');
$weekday_initial[__('Tuesday')]   = __('T');
$weekday_initial[__('Wednesday')] = __('W');
$weekday_initial[__('Thursday')]  = __('T');
$weekday_initial[__('Friday')]    = __('F');
$weekday_initial[__('Saturday')]  = __('S');

por

$weekday_initial[__('Sunday')]    = ('D');
$weekday_initial[__('Monday')]    = ('L');
$weekday_initial[__('Tuesday')]   = ('M');
$weekday_initial[__('Wednesday')] = ('X');
$weekday_initial[__('Thursday')]  = ('J');
$weekday_initial[__('Friday')]    = ('V');
$weekday_initial[__('Saturday')]  = ('S');