Is there any bad side effects for using calcium chloride to replace a running dehumidifier?
As for safety, calcium chloride, $\ce{CaCl2}$, is in sea water and added to foods, such as beans and pickles. It's about as dangerous as table salt, sodium chloride, $\ce{NaCl}$ (actually, $\ce{CaCl2}$ is safer for concrete).

However, it absorbs only so much water until it dissolves and stops being effective. What would you do with the puddle of $\ce{CaCl2}$ solution? It can be dried with heat and reused, but then your just moving energy usage from a continually running electric dehumidifier to a batch process using $\ce{CaCl2}$... though if you can get heat for free, it would be cost effective! If you don't have a solar concentrator or access to geothermal energy, there would probably be no energy savings, though.