Each stadium features various objects (these include statues, sculptures, floating skill icons, and screens).
Hitting any of these "objects" will yield various bonus points during matches.
The game distinguishes between 2 main types of objects.

[ Jumbo "Scoreboard" Screens & Floating "Skill Object" Icons ]

During matches, the jumbo screens and floating icons will light up with a specific skill.
Hitting them will not only yield bonus points, but will also activate a "skill" ball on your opponent.

If you can hit them, triggering skill balls on your opponent will distract their gameplay which can be used to your advantage.
Conversely, you should also avoid having these skills triggered on you by trying to hit the screen / icons first.

You can also equip "skill defense" cards which can block the skill from triggering (even if your opponent activated it) with a fixed chance. Each stadium features different sets of skills that can be triggered.

Knowing which skills are triggered in each stadium can be very useful and should be considered before entering matches!
(they are shown under the info pane for each 1vs1 stadium)

[ Miscellaneous "Symbol" Objects ]

These include all non-skill objects including monuments, statues, and sculptures found throughout each stadium.
Hitting a "symbol" object will yield bonus points (but does not trigger any skills).