"the velocity of the block is constant, so the net force acting on the block must be zero. thus the normal force equals the weight and the force of friction equals the applied force" what, if anything, is wrong with this statement

Explanation:

"the velocity of the block is constant, so the net force acting on the block must be zero. Thus the normal force equals the weight and the force of friction equals the applied force" The only thing which is wrongly stated here is that the normal force equals the weight. Normal force is not always equal to weight. If external force is applied at some angle with the horizon , normal force may be more or less than weight. Even in case of an object placed on an  inclined plane , weight is not equal to normal force .

All other parts of the statement are correct.