I can NOT reproduce the issue on MacOS X 10.7 

Here is the output of my console

$ php -v
PHP 5.3.16 (cli) (built: Aug 17 2012 11:13:15) 
Copyright (c) 1997-2012 The PHP Group
Zend Engine v2.3.0, Copyright (c) 1998-2012 Zend Technologies
    with Xdebug v2.2.1, Copyright (c) 2002-2012, by Derick Rethans

$ cat /tmp/datetest.php
<?php
$date1 = 1352012400;
//$date2 = $date1 + 86400 which should be next day
$date2 = 1352098801;
echo "date1: " . date ("Y-m-d_h:i:s", $date1) . "\n";
echo "date2: " . date ("Y-m-d_h:i:s", $date2) . "\n";

$ php -f /tmp/datetest.php 
date1: 2012-11-04_08:00:00
date2: 2012-11-05_08:00:01

$ php -v
PHP 5.3.2-1ubuntu4.17 with Suhosin-Patch (cli) (built: Jun 19 2012 03:21:35) 
Copyright (c) 1997-2009 The PHP Group
Zend Engine v2.3.0, Copyright (c) 1998-2010 Zend Technologies
    with Suhosin v0.9.29, Copyright (c) 2007, by SektionEins GmbH

$ cat date.php 
<?php
$date1 = 1352012400;
//$date2 = $date1 + 86400 which should be next day
$date2 = 1352098801;
echo "date1: " . date ("Y-m-d_h:i:s", $date1) . "\n";
echo "date2: " . date ("Y-m-d_h:i:s", $date2) . "\n";
//Output
//date1: 2012-11-04_12:00:00
//date2: 2012-11-04_11:00:01
?>

$php date.php 
date1: 2012-11-04_12:00:00
date2: 2012-11-04_11:00:01

Similar behavior on Mac OS 10.8 with PHP PHP (MAMP) 5.3.2 (cli) (built: Mar  5 
2010 16:45:34)

What time zone do you have set?

You have discovered Daylight Savings Time. DST changes the first Sunday in 
November which is Nov.4. Your output looks very wrong because you are using 'h' 
instead of 'H' so you are printing 12-hour hours instead of 24. Make it an 'H' 
instead and you will see they are 23 hours apart. Adding 24*3600 over a DST 
change is going to change the time by either 23 or 25 hours, never 24. This is 
why we have DateTime::add()