My cat tree is wobbly / Is it normal for my freestyle cat tree to move?

When all components are assembled and tightened a small amount of movement is to be expected in the pole. It's worth noting that the setup is perfectly safe with this wobble. In certain configurations, this could be due to the necessary clearances between the separate components and the high leverage force from the larger platforms. 

A slight rotational movement can't be prevented completely with a setup that has got one vertical pole only. In order to decrease the movement of the pole we can advise adding a wall brace to your setup, this will not stop the movement completely but will certainly help to reduce it. 

Another option would be to go for a two pole setup and connect them with a horizontal pole, a bridge or a ramp. This connection will stop the rotational movement.