Has anyone come across some software that allows an admin to view the activities of each port in the switch in a LAN ?
Yes, this is possible and an available option on most business class switches. The protocol that you would most likely use to cull this information from the switch is SNMP. Look for a good SNMP collector that has the features you want.
For example, have a look at Orion's NPM (expensive) or even look at the FOSS Cacti. If your switch supports netflow/sflow, that might offer you some of the type of information you're interested in. For example, InMon offers a free sFlow tool. Plenty of other sFlow/NetFlow tools are out there.
If you could supply us with more information such as the size of your environment, some of the specific things you want to monitor for and what type of switches you have, we could provide more detailed information.