What is arguably the major disadvantage of a parallel circuit is that as you add more and more things in parallel, the current draw on the source goes up and up and up. If the source cannot supply the current that is "demanded" by the devices all strapped across the so-called "rails" of the circuit, the voltage will (must!) decrease. This could be very bad, as some devices, notably motors, don't like to run at low voltage and can actually be damaged if voltage sags too much and they don't have undervoltage protection.
Fortunately, we have a pretty good power grid in many places, and this isn't a problem. Additionally, many devices have undervoltage protection built in, and they'll "trip" and shut down if voltages sag to a preset threshold.