Please create a new ticket for this if necessary, this issue is solved.

Yes, with your fix the errors from my first post are gone. And most of 
the time it works now. Thanks!

Maybe your're right with the remote calendars. The account that I use 
to debug the error is only a test account but someone has shared two 
calendars with this account and I didn't recognized it.

Some other users also had this problem I will communicate with them 
and give you a feedback if your fix also solves their problems.

Have the SQL errors gone now at least?

The log file doesn't help much because it contains only a tiny snippet 
of logs run within the same second.
This very much sounds like  you have some remote calendar that doesn't 
load or time out.

The calendar loads in the left sidebar. The error message is a simple 
German to English translation from a red popup in the right lower 
corner.

Regardless of the calendar loads or not - in both cases it tooks very 
long until the calendar loads or the error popup appears - and it's 
only an empty calendar without any events.
It's a bit different to locate related output in the log files because 
only with debug log level there's something. Maybe the attached file 
helps.

What happens in 1 of 10 times? Also, where do you get this message? 
What's in your logs?

Thanks for your fast support!
Unfortunately not: now it tooks very long to load the calendars in the 
left sidebar.  In 9 of 10 times it failes with an  error message like 
"failure while communicating with the server".

I don't know if it's relevant but we use Horde with a mysql database.

Does this fix it?

Changes have been made in Git (master):

commit 0e9a737b83f1742057429e9d5ca438dcb745bec3
Author: Jan Schneider <jan@horde.org>
Date:   Tue Mar 31 18:54:27 2015 +0200

     Make sure the user name is a string (Bug #13934).

  framework/Prefs/lib/Horde/Prefs/Storage/Base.php |    2 +-
  1 files changed, 1 insertions(+), 1 deletions(-)

http://github.com/horde/horde/commit/0e9a737b83f1742057429e9d5ca438dcb745bec3

Dear Horde developers,

we use Debian's Horde package. On occasion some users have problems to 
access their calendars. The problems occurs with Horde's webinterface 
and a standalone client like Thunderbird.
Trying to open the calendar results in the following error message:

[kronolith] SQL QUERY FAILED: SQLSTATE[42883]: Undefined function: 7 
ERROR:  operator does not exist: character varying = integer#012ZEILE 
1: ..._name, pref_value FROM horde_prefs WHERE pref_uid = 11988 
AN...#012                                                               
^#012TIP:  No operator matches the given name and argument type(s). 
You might need to add explicit type casts.  #012#011SELECT pref_name, 
pref_value FROM horde_prefs WHERE pref_uid = 11988#012#011  AND 
pref_scope = 'kronolith' [pid 14947 on line 204 of 
"/usr/share/php/Horde/Db/Adapter/Pdo/Base.php"]

Any hint what we can do to solve this?

Thanks a lot.