Which 1600 Dutch invention was refused a patent because too many people claimed it?

The telescope. Hans Lipperhey applied in 1608, and within weeks two other Dutch spectacle-makers were claiming the same thing; the States General decided nobody could own something so easy to copy, gave him money to build binocular versions instead, and the design was across Europe within a year.

Galileo heard about it in Venice in 1609, built his own without having seen one, and did the thing the Dutch had not: pointed it up. Within months he had mountains on the Moon, four satellites of Jupiter, the phases of Venus and the resolution of the Milky Way into stars - and the phases of Venus in particular could not be reconciled with the Earth-centred model.

He also understood the commercial pitch. His first demonstration was from a Venetian bell tower to the Senate, showing ships approaching hours before they were visible, which for a maritime republic was worth money and got his salary doubled. The optics were poor by any later standard - a narrow field, heavy distortion, magnification around 20 - and he was going blind by the end, possibly from looking at the Sun.