That would be a key piece of data. Oily residue doesn't sound good.

Put the heater on high. Remove the bleed screw. Fill the cooling system. Run it until no air comes out the bleed screw.

If that doesn't work, it is time to pressure test the cooling system.

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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