When selecting which picture to show to Oak, there is a button that says "Album Mark". Pick this and put a mark on the pictures you want to save in the Pokémon Album. This is a personal album unaffected by the Pokémon Report. These can be pictures of Pokémon you like that you don't think will score well, that you think will score well but want to save in case you take a better photo in the future, or even just of scenery that does not have any Pokémon in them. When you go to Prof. Oak, the pictures will be saved.
Once you are back at the laboratory you can select the PKMN Album option to view your saved photos. Here you can enlarge the photos, arrange their order in the album, and delete images you no longer wish to keep. There is a limit of 60 pictures in the album, so you may need to delete some if you want to save more images. You can also leave personal comments on each of the pictures.