The coordination of tissue function is mediated by gap junctions (GJs) that enable direct cell–cell transfer of metabolic and electric signals. GJs are formed by connexins of which Cx43 is most widespread in the human body. In the brain, Cx43 GJs are mostly found in astroglia where they coordinate the propagation of Ca2+ waves, spatial K+ buffering, and distribution of glucose. Beyond its role in direct intercellular communication, Cx43 also forms unapposed, non-junctional hemichannels in the plasma membrane of glial cells. These allow the passage of several neuro- and gliotransmitters that may, combined with downstream paracrine signaling, complement direct GJ communication among glial cells and sustain glial-neuronal signaling. Mutations in the GJA1 gene encoding Cx43 have been identified in a rare, mostly autosomal dominant syndrome called oculodentodigital dysplasia (ODDD). ODDD patients display a pleiotropic phenotype reflected by eye, hand, teeth, and foot abnormalities, as well as craniofacial and bone malformations. Remarkably, neurological symptoms such as dysarthria, neurogenic bladder (manifested as urinary incontinence), spasticity or muscle weakness, ataxia, and epilepsy are other prominent features observed in ODDD patients. Over 10 mutations detected in patients diagnosed with neurological disorders are associated with altered functionality of Cx43 GJs/hemichannels, but the link between ODDD-related abnormal channel activities and neurologic phenotype is still elusive. Here, we present an overview on the nature of the mutants conveying structural and functional changes of Cx43 channels and discuss available evidence for aberrant Cx43 GJ and hemichannel function. In a final step, we examine the possibilities of how channel dysfunction may lead to some of the neurological manifestations of ODDD.