Black specks appear above the blue area on the blue and white (BW) porcelain ware. Quite often they were found on the surface of BW porcelain.  But if there was no black speck on the surface, this could not say this is modern production.

Black specks (also called as iron spots) could show with different size. Some of them could be detected by naked eyes. Normally, 50x of magnification is enough for us to see the black specks.

If we need detailed structure, we have to use higher magnification.  Under the 200x of magnification, we can see that there exits dark transition zone between the black speck and the glaze (see the orange arrow on the photos) with the normal light.

Black specks from Ming period.

Black specks from Qing Period.

With Yuan blue and white porcelain ware, the black specks showed reticular or ribbon structure (see the arrow on the photos), which is distinguishable from those successors of late Ming and Qing period.

More detailed photos from Yuan period show here.

In the modern industrial porcelain production, normally, there is no problem of black speck any more due to the purity of the cobalt ores. But for the imitating modern blue and white porcelain ware, there is no such transition zone between the black speck and the glaze.