I'm new to blender so I may be just missing something simple. The bed frame in my low poly bedroom design from a tutorial I'm following has bad shadows on the top and bottom frames. This is when using Cycles.
Your mirror modifier on the bed frame has the Y-Axis Mirror enabled, which causes overlapping geometry since the object is whole and on its origin point on the Y-Axis, disable the Y-Axis Mirror by clicking on the Y to disable it.
This glitch is called "Z Fighting." It occurs when there are multiple faces in the exact same position. In your case, it looks like the Mirror modifier was mistakenly set to mirror in the X and Y direction.
Simply turn off the Y mirroring and the problem should be solved.