All wiper arms have a hinge at the base that allows the arm to flex as it follows the curvature of the window. If the wiper skips over certain spots, even with a new blade, chances are the hinge is binding from corrosion. It's most common on rear window wipers since they're used less often.
You can oil the hinge, but that's just a temporary fix—the corrosion and binding usually return. To fix the problem permanently, replace the wiper arm (available at an auto parts store).
All wiper arms fit onto a splined shaft (Photo 1). Some are held in place with a nut. To replace that type, just lift the protective cap, remove the nut and pull off the arm (Photo 2).
The other type is held in place with a locking clip. Unlock it as shown in the bottom photo and install the new arm (Photo 3).