Challenging decision problems in changeable spaces are characterized by existence of complex decision parameters that are changing with time and situations, including criteria and alternatives. Some of these parameters may be critical for their effective solutions, but hidden in the depth of potential domains. In this rapidly changing world, including technology and attitude, without paying attention to the problems in changeable spaces, we could easily commit serious mistakes due to decision blinds, decision traps and/or decision shocks. The article starts with a brief description of the evolution of MCDM toward challenging problems in changeable spaces. Then it briefly sketches a dynamic human behavior mechanism and habitual domain theory which provide an effective list for us to search relevant decision parameters and pave the way for latter discussion. Competence set analysis, derived from habitual domain, is then introduced to exemplify decision blinds, decision traps and decision shocks in challenging decision problems. Checking lists and methods for discovering blinds and traps and for dealing with shocks are also provided. Innovation dynamics, a systematic network of thoughts, is introduced to further look out relevant key parameters in dynamic challenging problems. The related academic subjects in each link of the innovation dynamics are also explained, which allow us to see the complexity and interconnectivities among different challenging problems in changeable spaces. Finally we introduce three habitual domain tool boxes to empower ourselves to expand and enrich our thoughts into the depth of the potential domains of the challenging problems, which allows us to more effectively identify hidden parameters, problems and competence sets to reduce decision blinds, avoid decision traps and solve the problems, or dissolve the problems before they occur.