The problem is that after I have clicked on a photo in a cluster and clicked on the "..." in the upper right corner of the screen, the option "set as a cover photo" is not listed (there is only "Add To", "Delete", "Show/Hide Info", etc.).
I found a workaround to the problem. On my iPhone I delete around 10 of the best similar photos from the people view associated with the person I want to correct. After a few minutes (5-10) I scroll down through the list of people view and I see the 10 deleted photos under an unnamed profile. When I click on that profile I give it the same name as the original profile and the app suggests to merge the two proviles together. After the merge the photo is updated with one of the 10 pictures I previously deleted. It is tidious but it seems to be the only way to do it on the mobile version of the app.
Is there anyway we can vote for this feature to be implemented more easily in the mobile app?