Вывод ошибки pyqt5

Assuming you are in a QWidget from which you want to display an error message, you can simply use QMessageBox.critical(self, "Title", "Message"), replace self by another (main widget for example) if you are not is a QWidget class.

Edit: even if you are not in a QWidget (or don’t want to inherit from it), you can just use None as parent with for instance QMessageBox.critical(None, "Title", "Message").

Edit, here is an example of how to use it:

# -*-coding:utf-8 -*

from PyQt5.QtWidgets import QApplication, QMessageBox
import sys

# In this example, success is False by default, and
#  - If you press Cancel, it will ends with False,
#  - If you press Retry until i = 3, it will end with True


expectedVal = 3


def MyFunction(val: int) -> bool:
    return val == expectedVal


app = QApplication(sys.argv)
i = 1
success = MyFunction(i)
while not success:
    # Popup with several buttons, manage below depending on choice
    choice = QMessageBox.critical(None,
                                  "Error",
                                  "i ({}) is not expected val ({})".format(i, expectedVal),
                                  QMessageBox.Retry | QMessageBox.Cancel)
    if choice == QMessageBox.Retry:
        i += 1
        print("Retry with i = {}".format(i))
        success = MyFunction(i)
    else:
        print("Cancel")
        break

if success:
    # Standard popup with only OK button
    QMessageBox.information(None, "Result", "Success is {}".format(success))
else:
    # Standard popup with only OK button
    QMessageBox.critical(None, "Result", "Success is {}".format(success))

Вы должны использовать excepthook,
и если вы хотите, чтобы событие завершилось, вы должны вызвать метод quit().

import sys
import traceback
from PyQt5 import QtWidgets, QtGui, QtCore


class ErrorApp(QtWidgets.QMainWindow):
    def __init__(self):
        super().__init__()
        bar = self.menuBar()
        menu = bar.addMenu('&Menu')

        action_raise = QtWidgets.QAction("Raise", self)
        action_exit = QtWidgets.QAction("Exit", self)
        menu.addAction(action_raise)
        menu.addAction(action_exit)

        action_exit.triggered.connect(self.quit_trigger)
        action_raise.triggered.connect(self.raise_error)

    def raise_error(self):
        aa = 5 / 0                                        # какая-то ошибка           

    def quit_trigger(self):
        QtWidgets.qApp.quit()



def excepthook(exc_type, exc_value, exc_tb):
    tb = "".join(traceback.format_exception(exc_type, exc_value, exc_tb))
    print("Oбнаружена ошибка !:", tb)
#    QtWidgets.QApplication.quit()             # !!! если вы хотите, чтобы событие завершилось


sys.excepthook = excepthook

if __name__ == '__main__':
    app = QtWidgets.QApplication(sys.argv)

    w = ErrorApp()
    w.show()
    sys.exit(app.exec_())