It'd be nice to have a quick dialog cutscene when the player gets the first visual contact to a UFO crash site to make it feel a more special moment. Currently the game doesn't even register it in any way and it makes it feel totally mundane. Add some fear of unknown and awe of humanity seeing something so unbelievable the very first time.
You could add similar dialogs every time a new UFO type is found to describe it a bit.. add a bit of mystery and flair to raiding them.
There needs to be a dialog when an alien you need to capture is found.
Generally speaking, the dialog cutscenes pretty much just stop coming after the Cleaner arc is finished, making the rest of the game lose a lot of flair. I'd love to see them at the beginning of every new mission type: terror, alien base etc.