When using the mechanical Velocity condition to you may get conflicts if it is located next to a no-slip condition (a wall). To remedy this you can exclude the common edge or point.
When using the Periodic Condition you may get conflicts or duplicates which makes the model either overconstrained, or problematic for the automatic constraint elimination algorithm. If you are aware of such situations, it is good practice to remove one of the potentially conflicting constraints. This could be in multiphysics models where you combine solid mechanics with thermoviscous acoustics and have edges where you both apply a periodic condition (solid and thermoviscous acoustics) and the Thermoviscous Acoustic- Structure Boundary multiphysics coupling.