is this the same / caused by 0006240 ?

Yes, it looks like 0006240. Sorry, I haven't seen it.
But I don't believe that the format is the same and I don't think that patch from 6240 will work in my case. In 6240 it is about additional ' characters which is not my case. In my case the string that comes from the DB is in different format. I checked the PHP and Mantis settings and they were OK, but the problem still existed. I will also stress that the same source worked under Windows Server 2003 and after copying it to Debian this problem occured, so I suppose that the PHP under Windows and under Linux give different things.

Here is my patch:
function db_unixtimestamp( $p_date=null ) {
global $g_db;

            if ( null !== $p_date ) {
                    $p_timestamp = $g_db->UnixTimeStamp($p_date);
                    $t_db_type = config_get( 'db_type' );
                    if ( $t_db_type == 'mssql' ) {
                            $p_timestamp = strtotime($p_date);
                    }
            } else {
                    $p_timestamp = time();
            }
            return $p_timestamp ;
    }

If you did not actually try, I would appreciate if you could test the fix in 0006240 and let us know if that works.

The problems are different, thou in the same place. The 6240 cannot help me because I don't have problem with apostrophies, but with the format. I don't think strtotime() can handle the apostrophies, and it works for me.
I can't make test, because our Mantis is in production...

1.2.x stores dates as int's [to get avoid issues like this]

MantisBT currently supports Mysql and has support for other database engines.

The support for other databases is known to be problematic.

Having implemented the current database layer into Mantis 10 years ago, I'm currently working on replacing the current layer.

If you are interested in using Mantis with non-mysql databases - for example, Oracle, PGSQL or MSSQL, and would be willing to help out testing the new database layer, please drop me an email at paul@mantisforge.org

In the meantime, I'd advise running Mantis with Mysql Only to avoid issues.

Thanks
Paul