Does trace mitral valve regurgitation cause shortness of breath and palpitations?

No: No, it must be much worse to do that.

Mitral regurgitation: Trace mitral regurgitation means that only a very small amount of additional blood volume is stressing the heart, this is usually not significant. For mitral regurgitation to cause shortness of breath it has to be a significant amount say 30% or more of each contraction. Palpitations can happen with minimal mitral regurgitation.

Mitral regurgitation: In general no, but consult your doctor if you are having symptoms.