Continuity mistake: When "Charlie" is first introduced to the class, she struts down the aisle in heels. When she follows Maverick into the building, you can briefly see that she is wearing flats to compensate for Maverick's short stature.
Visible crew/equipment: When they return to Enterprise after their successful mission, Iceman points and shouts, "You!" at Maverick. In the shot facing Maverick as he turns his head, the reflections of the camera and large reflector screen are visible on Maverick's sunglasses. Also, note the lack of a crowd of people behind Ice in the reflection. (01:40:45)
Visible crew/equipment: During Cougar's standoff with the MiG, Maverick comes in to assist him. Right after he says "I'm on my way" a few cuts happen then we see the right (or starboard in the Navy) of Maverick and Goose's F-14 along with the canopy. A camera can be seen in front of the copilot, onto of his instrument console.
Chosen answer: The term "Ghostrider" refers to the squadron name. There used to be a Tomcat squadron called the Ghostriders. Usually in a radio call, the squadron name is followed by a number. For instance, in the first fight where we see Cougar get into a spot of trouble with the Mig on his tail, he radios "This is Ghostrider 117 this bogey's all over me, he's got missile lock on me, do I have permission to fire?" That is normally the correct term as to who is on the radio.