Seeing the reported speeds, especially 10 Mbps, I'd say bad cabling. Or do you actually have devices that are only able to do 10 Mbps?
You could try doing a "configure ports auto on speed 10 duplex half" and see if this reduces link flapping, especially for the ports that connect using 1 Gbps right now. If it helps, cabling is very likely to be the cause. But attention: 10 Mbps half-duplex won't make your users happy, as this is veeery slow. And you actually need to dis- and re-enable the ports to force the new setting.
