I can confirm the double notifications (and there is a different thread about this).
And there is this thing that clicking on a notifications does not lead anywhere. I interpret that as a notification of a listing that has review status. It is stupidity that THS is sending out such notifications, they are annoying their customers with missed opportunities and it only contributes to the moaning on this forum about the limit-of-five and to general dissatisfaction with the company. I had started a thread about this in October: Question: why send alerts for sits that are under review
But on my iPhone, the app is stable and does not crash.
Edited: the double notifications are still coming in.