That got me thinking, is that a record for the quantity of a single piece that appears in a set? It's actually not that easy to find out...
The reason it's not so easy to determine is that the inventories that LEGO publish max out at 200 of any one piece for some reason, so our inventory data, which we obtain from there, won't help.
I therefore headed to BrickLink to do some research there. The community-generated inventories there tend to be more accurate but I don't think there's a way to find out what I'm looking for without having some idea of likely candidates and manually checking.
Large Technic sets often contains hundreds of pins, particularly the black 2l friction pin, so there's another place to check. It's easy to see which sets contain the most by sorting the list at BrickLink and it turns out that 42055 Bucket Wheel Excavator, the second largest Technic set to date, contains 724 of them, which might therefore be the record.
Unless, that is, you know better? Can you think of any other sets that contain hundreds of the same piece? More that 724? Let us know in the comments.