Botox has a number of applications/uses in the neck. The main cosmetic uses are for muscle bands that run from under the chin, called platysma bands. Botox can also soften horizontal lines in the lower neck. There were a few reports of patients having swallowing difficulties in the early studies. However, this was using over 100 units of Botox. If your treating physician uses under 100 units, I don't use more than 60 units in the neck, it is very safe and there have been no reported complications from cosmetic Botox.
There have been some reports of complications following injection of Botox into the neck but these were associated with neck muscles in the back which can cause painful spasms and require extremely large doses.The use of Botox for cosmetic control of neck bands requires significantly less and if performed properly, by an educated and experienced professional, are extremely safe.