When Danny, Sam and Tucker come to Ember's midnight concert, they are intangible as they come up out of the ground. Neither Sam nor Tucker are touching Danny as this happens. Normally, Danny needs to be in contact with someone to make them intangible along with him.
After Tucker is disconnected from the computerized test trainer, he mentions the word "volume", then mechanically states the volume for a sphere. However, the formula he quotes is actually for the volume of a circular cylinder.