Meaning of SSMS database icon preceded by scroll with red x
This is documented in BOL under "Administering Servers by Using Policy-Based Management"


  For failed policies, Object Explorer indicates a critical health
  warning as a red icon next to the target and the nodes that are higher
  in the Object Explorer tree.


I've not used policy based management myself so am not entirely clear what this means. Through the UI I couldn't see any way of denoting a policy condition as having any particular severity.

I've made this answer community wiki in case someone more familiar with the subject area wants to expand upon it.