The opening shot show's Tony's house in the daylight but when Tony wakes up Jeannie she exclaims that it's 4 in the morning. There is no possible way it could be daylight in Cocoa Beach, Florida at 4 in the morning.
When the Blue Djinn comes out of the ocean much of the blue paint has been washed off.
In the wide shot of the beach and some closeup shots, you can clearly see utility lines and a pole above and behind the trees from Verdugo Avenue, just outside the Columbia Ranch facilities.
In the launch pad / launching sequence, the rocket involved changes from a Gemini-Titan to a Delta to an Atlas-Agena in the various scenes.
In the new animated opening credits for season 2, Jeannie uncorks the bottle from the inside and exits. However, she's not supposed to be able to free herself. Being freed by someone is what makes her indebted to be their genie. This could have been corrected by the animator when the hatch of the space capsule opens and hits the bottle, it should have knocked out the cork, thereby releasing the genie.
When the Blue Djinn arises out of the water holding the vacuum cleaner, there is a set of buildings reflecting in the water behind him. The water is supposed to be a vast ocean as far as the eye could see.