We were having that same error. After debugging the response, as Gareth J Barnard suggests, we discovered that the problem was that "Debugging emails" was set to active in the site configuration. If this setting is active, the response after a new message is posted is a list of SMTP related messages, which are not valid JSON.
After deactivating the debugging emails option, the error disappeared and the messages plugin works as expected, without the need to reload the page with every message.
Kind regards.