This might not work (or-ing multiple errors) if you do not define them as bit-values but plain enums. Since you evaluate the bits in KSettingsOnlineQuotes::setupIcons(), I suggest you use

class Errors {
  public:
    enum Type {
      None =       0x00000000,
      Data =       0x00000001,
      Date =       0x00000002,
      DateFormat = 0x00000004,
      Price =      0x00000008,
      Script =     0x00000010,
      Source =     0x00000020,
      Symbol =     0x00000040,
      Success =    0x00000080,
      URL =        0x00000100
    };

as defintion for the enum.

Can we have named constants (enums) for the states please?

I would write this function as:

void KSettingsOnlineQuotes::slotLogQuote(const QString &id, const QString &symbol, const QString &date, double price)
{
  slotLogStatus(QString("%1 %2 %3 %4").arg(id, symbol, date).arg(price));
}

It avoid code duplication. The optimizer should take care of the alleged overhead here very well.

A hint to the forum at https://forum.kde.org/viewforum.php?f=69 might also be valuable.

Does this really describe the date format?

I see some potential problem here that once noError is used in a method call as default and an error occurs, noError will keep the error for as long as the application lives. Use a temporary in the case of default value for parameters to avoid this, e.g.

bool launch(const QString& _symbol, const QString& _id, const QString& _source = QString(), Errors &_errors = Errors());

as you do with QStrings already.

The fun of operator overloading. I did not spot this but you're right. Case closed.