If the packages have an exposed pad, and if you haven't already, check whether some pins are shorted to ground (which is probably what the exposed pad is connected to). If so, you'll have a very hard time getting rid of the shorts with just some manual touch-up.
The solder paste mask matters. Is your exposed pad area in the stencil a solid square, or is it several smaller squares (as shown here:
https://www.allaboutcircuits.com/technical-articles/stencil-design-for-exposed-pad-packages/ ) The latter is a much better approach to avoid shorts and flatness issues.