I've received an email asking to revisit Jo Jo cookie jars. The key things to look at are the ball and the bottom. The ball is yellow on vintage jars and the bottoms are as pictured below. The fake jars have fake crazing as pictured.
The ball on this jar has brown over -spray from the painting of the seal.
Multi colored ball
If there isn't a picture of the bottom - ASK. Also on vintage jars - determine if the ball has been glued on, the line is usually obvious. This is a common flaw with these jars.