Was the shutter speed the only thing that changed, or did you change the aperture, too?
At smaller apertures (higher f/ number), dust near the focal plane is easier to see than at larger apertures. This is typically a problem at (my guesstimate) f/10 and smaller).
This effect is used to find dust specks on a sensor:
Take a shot of a uniformly lit, evenly colored surface (a clear blue daylight sky works fine), at minimum aperture.
Dust specks should be easily apparent, if they are there.