... inaccurate stress concentrations at the weld shell connection to the solid.
This is because there are singular results at the connection between solid and shell elements. Multipoint constraint equations (or 'links' which show up as those pink lines) are required to connection solid to shell elements due to the nodal incompatibility that exists between the two; that is, solid elements have only three DOF (all translation) while shell elements have six DOF.
It's unrealistic to try and get accurate stress results in the area directly occupied by a weld. It's more realistic to look at the stress results in the material near the weld (but not within it) and/or look at the internal forces within the weld and compare them against analytical methods. Also keep in mind that, unless you have a full penetration weld, you need to consider fracture mechanics when trying to determine if a weld is good enough.