As far as I can tell, visit_first_action_time is stored in the database in UTC, the Live visitor log, however, does not account for that (or does so insufficiently) in the WHERE clause.
For example: I have a website on UTC+02:00, and I had a visitor at 23:05. So this visitor was displayed, when the day of the recorded server time was selected in the calendar, however the displayed time was corrected for the timezone, which gave a very interesting effect: instead of displaying as 2010/10/13 23:05 it was displayed as 2010/10/14 01:05. After selecting 2010/10/14 in the calendar, it was not displayed at all.

The following patch needs to be applied, to make the visitors show up at the day they visited by the website timezone, not server time (description fits on trunk-r3248):

* plugins/Live/API.php  
  modify function loadLastVisitorDetailsFromDatabase, replace 
  $processedDate = Piwik_Date::factory($date,$currentTimezone);
  with
  $processedDate = Piwik_Date::factory($date)->setTimezone($currentTimezone);

  modify function loadLastVisitorDetailsFromDatabase, replace
  array_push(  $whereBind,
    $processedPeriod->getDateStart()->toString(),
    $processedPeriod->getDateEnd()->addDay(1)->toString());

  with
  array_push(  $whereBind,
    $processedPeriod->getDateStart()->toString('Y-m-d H:m:s'),
    $processedPeriod->getDateEnd()->addDay(1)->toString('Y-m-d H:m:s'));