Even though Dr. Smith's plant which has attached itself to the top of the J2 has grown so big to clog up the intake vents, when we see exterior shots of the J2 avoiding missiles and releasing the Pod the plant is nowhere to be seen.
Dr Smith is in his cabin with his plant, when the plant is shown to have grown bigger and come alive. After the opening credits, Smith is shown on the main deck with John and Don. Only when Smith returns to his cabin, does he notice how much the plant has grown. Smith would not have been able to leave his cabin, in the first place, without noticing the giant plant, at that time.
The professor explains that the alien plant is causing trouble for the Jupiter by clogging up the air vents. In deep space, there is no air to circulate in such a vent.
While evading a missile fired from the planet below, Professor Robinson has to extinguish some sparks in the rear of the top deck. However, the stair rungs indicate they are really on the bottom deck as they do not go down any farther.
Given the rate of speed which the J2 was traveling, it would be physically impossible for Dr. Smith's plant to attach itself to the J2 after being sucked into space via the hatch.
The Robot checks his math capabilities and states that 8 + 8 equals 37. Dr. Smith corrects him by saying 36 when he should have said 16.