The boom can be seen reflected in the mirror in Lwaxanna's guest quarters as she talks to Deanna. A studio light is also reflected in the mirror. The shadow of the boom is then visible against the wall as Lwaxanna walks towards Deanna.
The suggestion in the episode that the star would need to reach a constant core temperature of 220 MK is absolutely misinformed. This could never be a main sequence star, and it would constantly be ejecting large amounts of matter, or more likely immediately start the final phase of its life and explode (as it did in the episode when the temperature jumped another rather negligible amount)
When the Kaelon warships are sent to intercept the Enterprise, Picard orders Red Alert and shields up. Lwaxana then leads Timicin off the bridge. While Lwaxana and Timicin are discussing the situation in a corridor ringed with flashing Red Alert lights, Riker signals Timicin from the bridge that Timicin has a visitor (his daughter). The only way his daughter could have arrived so quickly is if she had beamed aboard. But it would have been impossible for her to beam aboard with the shields up.