The wheel should run true
- radially (up/down)
- axially (sideways)
- and should not be twisted (as each spoke applies force at its eyelet, a weakened rim might twist, and this twist might not be noticed whilst truing out axial deflections).
The form of the bead interface should be consistent, no dents in any direction (unless the rim is for tubular "stick-on" tyres, in which case it would not have a bead seat).
If the rim has a braking surface, it may have featured wear indicators. These would be either square-edged grooves or cylindrical indents.
If the braking surface has become concave, the rim wall connecting the bead interface to the well of the rim (where the spokes end) might be dangerously thin. A failure here would be characterised by a sudden separation of a metallic ribbon as the bead interface succumbs to the force applied by the tyre pressure, and the tube would expand through this new opening until the tension in the rubber exceeds its strength or the sharp edges of the broken metal pierce the tube.
The metal surrounding each eyelet should not be deformed. A wheel that has been repeatedly trued may have excessive tension on some of its spokes. A wheel with insufficient tension would not distribute loads appropriately as it rolls, causing spoke tension to fall an rise. Changes in tension cause deformation in the rim and spoke. Metals have a finite capacity for load cycles, ending with a fatigue failure.
The rim may tear at an eyelet, allowing the nipple to pull through and causing a sudden change in the tension distribution of the wheel, which may deflect enough to cause contact with the brake or frame. A complete localised loss of tension may also result in a load exceeding the capacity of an unsupported rim section, resulting in a catastrophic failure of the wheel and sudden changes to the trajectory of the rider.