Steve goes downstairs to fetch Jenny's doll. Then he helps fight monsters. The doll isn't seen again until he presents it to Jenny near the end. Update: The doll was actually in his back pocket throughout the movie. Not exactly recognizable as the doll, sometimes only some fabric was visible, similar to a handkerchief sticking out. Other times, much more could be seen.
When the "Vacuum Cleaner of Doom" flies through the living room window, the curtains are partially open. Later, when Steve goes downstairs to get Jenny's doll, the curtains are closed. The rest of the family hid in the upstairs bedroom, so no one else could have closed them.
Sometimes the "Vacuum Cleaner of Doom" is partially transparent, revealing items behind it.
The Small UFO stops and vaporizes a lead bullet, however it takes several minutes for the same UFO it to attempt to shoot thru a wooden bedroom door.