Any company is able to monitor what their customers do and how they act and react while using the business; this is no different for Square Mobile Payment. Google monitors and logs customer behavior data as does Amazon, companies watch for trends with consumers so they can react accordingly and tailor their business to meet their customer's needs.
Yes it is wrong to log customer behaviour data because customers have the right to privacy and protection of that data. Logging this information infringes on that right. The logged information could then be used to target individuals and spy on them without proper legal authority. Payments that customers receive or send out are personal transactions and should not be kept stored for future use.
While logging customer behavior can be considered taboo, it can also be beneficial when dealing with your repeat customers. Knowing that Jim likes gluten free, or Jill loves extra bacon creates a sense of family on a very basic level. This can separate the little guys from the corporate giants who run as machines and lose touch with the human connection.
The Square Mobile Payment Device is by no means the only system that tracks customer behaviour, This kind of marketing has become the norm in modern society and it is essential for companies, if they wish to be successful, to use these kind of tools, This is especially the case if they wish to stay one step ahead of the competitors.