Is the Kekule structure of benzene completely wrong?
In benzene, all of the carbon-carbon bond lengths are equal.  Therefore, the Kekule structure shown below is an incorrect representation of benzene.



It is incorrect because it suggests that there are two different types of carbon-carbon bonds in benzene, a carbon-carbon double bond and a carbon-carbon single bond. Typically, the bond length in a carbon-carbon double bond is around 135 pm, a carbon-carbon single bond is around 147 pm long, while the carbon-carbon bond length in benzene is roughly in between at 140 pm.

Benzene is often drawn as follows to indicate that all of the carbon-carbon bonds have the same length and the pi electron system is continuous and uniformly distributed.



Sometimes, when one is discussing the resonance properties of benzene, two Kekule structures are drawn with the double headed resonance arrow between them as shown below.  This is meant to indicate that these two Kekule structures are resonance structures of benzene, and that taken together (e.g. in one Kekule structure a carbon-carbon bond is a single bond, in the other structure the same bond is a double bond; so "real" benzene is a simultaneous, superposition of these two structures where each carbon-carbon bond is in between a single and double bond), they represent the true electronic and physical structure of benzene.