I think there are a lot of myth-myths where basically the general public ran with a wildly pseudoscientific interpretation, and then the scientific community decides to dismiss the entire thing (at least outside of whatever subfield, although I've sometimes seen it within too).
Speaking specifically to left vs right brain, in popular media I've mostly seen it presented as logic vs creativity, which completely disregards that people can be creative verbally, and that certain quantitative/technical things are very non-verbal.
The mirror neuron system is also a myth-myth. While there aren't "mirror neurons", per se (e.g., biochemically different), there is a system of mirroring and it is very important