Future Internet has been a hot topic for the last decade. One of the approaches put forward in order to revise the Internet architecture is LISP - Locator/ID Separation Protocol, which leverages the separation of the identifier and the locator roles of IP addresses. Contrary to the classical push model used by the BGP-based routing architecture, LISP relies on a pull model. In particular, routing information is pulled from a new network element, the Mapping System, to provide the association between the identifier (i.e., the address used to identify a host inside a domain) and a list of locators (i.e., the addresses to locate an attachment point) upon an explicit query. In this paper, we evaluate a LISP Mapping System deployment in the public LISP Beta Network from two standpoints: Stability and Consistency. Our measurements show that the mapping information is stable over time and consistent between the different mapping entities and the vantage points. Our analysis shows that there are cases where the Mapping System is unstable and/or inconsistent, hence, beside proposing a taxonomy in order to classify them, we carry out an in-depth investigation of such cases so to provide hints on how to improve the performance of LISP.