I too get a mismatch between a pattern's appearance in Inkscape and in pdf.
As a workaround I convert the pattern to objects ( Object -> Pattern -> Pattern to objects or Shift+Alt+I) then what you see on screen is what gets output to pdf.
That said, any transformations of the pattern beforehand make the operation hit or miss. E.g. If I fill a square with polka dots and change their appearance using the node handles the bunch of dots leap outside the box when I convert the pattern to objects.
Patterns are one of those great "timesavers" which can ultimately cost you hours of head and heartache. For your particular drawing I'd be tempted to use a tiled clone for the circles instead of a pattern.