Doesn't Slow/Rear Sync cause blurred shots?

Yes and no. 

When you shoot with flash, there are generally two exposures happening:

  1. the flash exposure on the subject
  2. the background ambient exposure

If flash is the main source of light, a stationary subject lit by it should always be sharp, as the slowest Nikon flash duration is about 1/830 of a second. 

The background, however, very well may go soft or get blurred by poor handholding technique or subject movement. Many photographers have learned to use this to their advantage—there's one style of flash that uses very long shutter speeds and panning/zooming/tilting to purposefully blur the background yet still use the flash to "freeze" the subject.

When the "balance" of light is split between ambient and flash, subject motion can create blurred edges.

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