I'm surprised no one has mentioned the missing shuttle craft in Galileo 7.
I just watched this episode last night and noticed that right away. When the Galileo is getting ready to launch, you can see the shuttle Columbus in the lower right corner of the scene, but when it shows Galileo leaving the shuttle bay, Columbus has vanished.
One shot I did like was the rear landing strut retracting after launch.
Also, I had to wonder, why they only launched one additional shuttle to help search for the Galileo? Wasn't the Enterprise supposed to have at least 4? For example, in The Omega Glory, it was mentioned that "all 4" of the shuttlecraft were still on board (The Exeter) so it implies that a Constitution class Starship would normally carry 4 shuttles.