Yes, this is very common with OSP boards and even more so if you are using a lead-free alloy. IPC 610 also supports this as a acceptable condition.

This is a common issue with Pb-free solder. For the most part, it depends upon your environment and your level of risk acceptability. For most applications, a small amount of exposed copper should have no influence on reliability.

Exposed copper around the periphery of the pads is acceptable.

With the use of the new lead free solder alloys the basis metal copper is at times visible around the periphery of the pads. This is due to the lack of wetting with new lead free alloys or differences between pad sizes and stencil aperture sizes where the paste deposition does not cover the entire pad location. In these cases the molten solder may not wet to the edges of the pad or land areas, yet this does not impact the reliability of the solder joint. 

Work conducted during the 80s proved that exposed copper is not a problem and will not deteriorate over time. It is important understand the need to verify the fluxes used are compatible with the end use of the product. Residual flux residues must be benign to not impact the long term reliability of the product and if the residual flux residues are not benign, then a cleaning process must be incorporated to clean the flux residues.

Hence, the reliability of the solder joint is based upon how the solder wet the basis metal and the lead, not how much of the pad area was covered with the molten solder. 

Many times customers relate this exposed copper to lack of solderability and must be educated in the physical behavior of fluxes and molten solder where the solder will not wet to the edges of the pads.