The safety concerns regarding flame-effect electric fireplaces are the same with space heaters. They shouldn't be left unattended. It's also critical to buy only the unit that comes with an auto shut down timer.
The length of the cord factor is another factor that's often overlooked by buyers. However, it's actually important as an extension lead would deem to be dangerous for electric fireplaces. So, make sure that the unit you choose comes with an electrical cord that can reach your power outlet.