Is that an multiple choice question?
I feel it should read: The inspector should inspect for connectors from solid fuel-burning appliances that have a rise to the chimney for less than 1/4-inch per foot and proper support.
A rise of less than 1/4"-inch per foot is a disallowed slope for a vent connector on solid fuel-burning appliances.
Solid fuels: Wood, Coal, or Pellets.
Solid fuel appliances: Wood stoves. Fireplaces. Specialized boilers and furnaces.
The standard installation requires a minimum slope of 1/4"-inch of rise for every foot or 12"-inches of horizontal run, is to ensure proper upward/upstream flow of combustion flue gases and to prevent dips or sags in the connector pipe.
Picture the horizontal run of stove pipe from an airtight wood stove or pellet stove (coal stove) to the chimney. That is what they are referring to, just eyeball it, does it have a little slope? your good.