If you are on iOS, you have nothing to worry about.
The problem was for Android phones with the current update (that included the fix for the berry bug). It introduced a new bug when tapping on a pokemon. Instead of just cutting to the encounter screen facing the pokemon, the camera starts facing a different direction and pans in to the pokemon. This panning either prevents you from seeing the sparkly-stars animation for shiny pokemon, or it is preventing the animation from playing altogether.
The shiny pokemon still correctly display their alternate colors, but some shiny pokemon have very subtle color differences.