Changes have been made in Git (FRAMEWORK_5_1):

commit f3fe42724404bc139668c582cc586abba67645f3
Author: Michael M Slusarz <slusarz@horde.org>
Date:   Mon Apr 7 14:06:48 2014 -0600

     Bug #13092: allow new mailbox name to be provided on spam page

  ingo/lib/Form/Spam.php |    1 +
  1 files changed, 1 insertions(+), 0 deletions(-)

http://github.com/horde/horde/commit/f3fe42724404bc139668c582cc586abba67645f3

Yes :-)

Does this fix?

Changes have been made in Git (master):

commit 8fa398a08020e44a3da986cc303f916154ef2f86
Author: Michael M Slusarz <slusarz@horde.org>
Date:   Mon Apr 7 14:06:48 2014 -0600

     Bug #13092: allow new mailbox name to be provided on spam page

  ingo/lib/Form/Spam.php |    1 +
  1 files changed, 1 insertions(+), 0 deletions(-)

http://github.com/horde/horde/commit/8fa398a08020e44a3da986cc303f916154ef2f86

Well, done. Actually the problem is what's being checked while 
returning from __isset() function in .\Horde\.Variables.php:

         return count($this->_expected)
             ? $this->_getExists($this->_expected, $varname, $value)
             : $this->_getExists($this->_vars, $varname, $value);

count($this->_expected) is equal to 3 so $this->_expected is checked 
instead of $this->_vars. Obviously folder_new name is missing from 
expected array.

Although I don't know how do you want to fix it so I don't provide a patch.

You'll have to debug exactly *why* the isset call is failing on that 
data in Horde_Variables then.  Since I can't reproduce.

It's pure ASCII.
Environment (i.e. static public function)?

Looking at the code (Horde_Variables), there should be no way that a 
get() call is successful when an isset() call is not.  Especially 
since the contents of that form ID is not an empty-ish value.  (The 
mailbox name doesn't happen to contain non-ASCII characters does it?)

I don't like to blame PHP versions... but nobody else is reporting 
this so I'm not sure what else could be the issue.

Then it doesn't work too (throws exception as before).
Actually OS is the newest CentOS 6 with php 5.3.28 coming from IUS repo.

Would you recommend upgrade to PHP 5.4? Would Horde work with this?

What if you change to:

if ($vars->exists($new_id))

(If that works, then it pretty much proves your PHP version is broken).

Just one final note:

this doesn't work (condition is false):

if (isset($vars->$new_id)) {

this does work (condition is true):

$vars_new_id = $vars->$new_id;
if (isset($vars_new_id)) {

Don't ask me why. I'm asking you :-)

Actually that was not easy. Only one line was found:

Could not validate IMAP mailbox. [pid 8036 on line 27 of 
"/usr/share/pear/Horde/Core/Notification/Handler/Decorator/Hordelog.php"]

I had to do some handjob with the code. This is what I've found:

Let's take line 128 of .\ingo\lib\Ingo.php:

        if (isset($vars->$new_id)) {

$vars->$new_id is equal to "newfoldernameIgave"

However,

  isset($vars->$new_id) evaluates to FALSE (!!!). Therefore mailbox is 
not created and validation fails.

Replacing line 128 by:

if ( true ) {

allows correct Spam folder creation.

In this case however "Save and disable" later produces another PHP error.

I hope you can sort it out properly.

Please follow the hints at 
http://wiki.horde.org/FAQ/Admin/Troubleshoot#wsod to generate and find 
a useful error message.
It's there, just not individually specified in the registry configuration.

Additionally, looking closer for the problem reason in 
./ingo/lib/Ingo.php I found:

- "if ($GLOBALS['registry']->hasMethod('mail/createMailbox') {}" 
expression doesn't return any true or false value, but produces white 
screen when called from the script or from the Horde admin PHP shell 
in Ingo context;

- also there is no "mail/createMailbox" method in the registry 
(although I can see other elements as "mail/blacklistFrom" or 
"mail/applyFilters" there).

We're using: horde 5.1.6, imp 6.1.7 and ingo 3.1.4

Ingo uses sieve as a backend. Other backends are disabled.

When I try to create spam rule that moves spam to a specific new   
mailbox, create new mailbox function doesn't work. An error "Could not 
  validate IMAP mailbox." is shown after trying to save new rule.

I can create new mailboxes via IMP or other mail clients, but not via INGO.

Managesieve shows debug output but there is no sign of mailbox 
creation attempt.

Looks like sieve protocol works because sieve scriipt is succesfully 
stored on IMAP server. Just the mailbox is not being created.

The problem looks very similar to http://bugs.horde.org/ticket/12174 .