Wrong space group
Sometimes crystal symmetry combines with non-crystallographic symmetry (NCS) and produces a diffraction pattern resembling higher symmetry space group than what you really have. NCS in this case closely resembles crystallographic symmetry. If resolution is not high enough, the difference in spot positions may be too small to give any detectable problems with indexing, integration and scaling. Even phasing (e.g. molecular replacement) may be successful. But if your R-factor hangs fairly high and you have problems building parts of your structure, it is worth trying to check other space groups. The most straightforward approach is to try processing data in P1, because if that does not bring R-factor down significantly, other space group choices will not solve the problem either.
This occurs most often at moderate resolution. However, the structure of the ketosteroid isomerase had to be refined in P1 at atomic resolution, although it refines well in C2221 at lower resolution such as 1.5A.