I haven't tried dry ice in kitchen equipment, but have destroyed a plastic measuring jug with liquid nitrogen (the scale had become illegible so I took it into work where it would be handy, then abused it). The failure mode could be expected to be relevant to plastic and glass used with dry ice.
Many plastics become brittle at low temperatures - this can ...
Not unique to dry ice, any kind of ice apparently dulls sharp blender blades over time. If you're going to crush any kind of ice, you should get dull square heavy blades or even specific "ice blades" for that purpose.
However, if you're just experimenting, that shouldn't be a problem just doing it once or twice.