My rear window washer always sprayed a stream and not a mist. There is a lot of discussion on here about it, many are the same way. I always figured out it was designed to flood the wiper, and reduce scratches from the grit on the rear window. I certainly wouldn't call it a major design flaw, that seems a bit extreme.

If the SES light isn't on, there isn't much to diagnose. I wouldn't worry about it.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue