On solder in vias: It looks like the via are not solder masked well and pick-up solder either: * Solder coating ... OR * During leveling
It's possible that the design specifies openings in the solder mask for these via.
On solder in the unsupported holes: Some residual material left behind from some direct metallization [DM] processes may be the culprit. After drill, holes are treated to accept electrolytic copper plating and may even get 'flashed' with a thin electrolytic copper plate. Non-plated holes are typically tented and protected from additional copper/tin plating when the dry film is applied for the pattern plate process. (tin for etch protection). During the etch process, most if not all of the copper plating or DM that may be in the non-plated holes gets removed. If not all is removed or if the residual DM is left in the hole, it is now susceptible to plating process.
On pads with no solder: Doesn't say much about the effectiveness of your fab's final inspection process does it?
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