Over the years, the CBA magazine has published many studies on the subject of cast bullet weight variation. Someone sorts their bullets by weight and shoots them for groups. Then they take unsorted bullets or reject bullets and shoot them for groups. 9 times out of 10, there is no difference. The other 1 time out of 10, the reject bullets are more accurate.
I don't sort by weight, have shot many sub-moa groups with unsorted cast bullets.
I used to merely inspect visually. If it looked good, I would shoot it.
Now I randomly check for as-cast diameter, too. Once in a while the mold doesn't close completely because of a spec of lead on the faces. Or, perhaps diameters are too small because the mold got a little hot. Though, usually that shows up at the reloading bench when you go to seat the gas check and size the bullet.
I can think of 4 things that cause weight variation:
1) internal voids, usually near the base.
2) incomplete fill
3) diameter variation due to temperature. Smokeless alloys are prone to heat shrink, BP alloys drop out bigger as the mold gets hotter.
4) diameter variation due to mold not closing completely.
Not much you can do about internal voids. The heavy big bore bullets almost always have internal voids, fact of life.
Incomplete fill can be judged by eye as they drop out of the mold. Rejects go in the sprue pot to be recycled.
With practice, you can judge heat shrink by shiny/frosty appearance.
Mold not closing completely can bite you. Every few pours, visually inspect mold faces for lead spatter, clean as necessary (only takes a second to knock off spatter with fine steel wool).
BTW, almost every mold that customers have returned for repair or alteration had lead spatter on the faces. I get the impression that the average caster is not terribly vigilant at cleaning spatter.
Getting a little off the subject, another problem I frequently see on returned molds is mold-prep type stuff on the mold faces. Mold-prep has a certain thickness and prevents the mold from closing completely, just like lead spatter. I do not recommend using mold-prep stuff on the mold faces. It causes problems and simply is not necessary. Save the mold prep stuff for the sprue plate and the top of the mold.
A 3 grain range on a 300 grain bullet is 1%. Seems reasonable to me, I don't think target shooters do much better than 1% unless they weigh every bullet and sort.