My employer requires employees to clock in on a time keeping system. The system does not record the exact time the employee arrives or departs. If we arrive and start working at 8:54 am it clocks us in at our scheduled shift start time of 9 am. If we depart at 5:05 it clocks us out at our scheduled shift end time of 5 pm. A few minutes before and after shift don't seem like a big deal but it adds up over time. I know rounding is permissible if the rounding averages out but since this time keeping software has been implemented all the employees are losing a few minutes here and there both before and after shift.

The solution given to us is that if the situation described above occurs we are to notify the person in charge of scheduling via email. This would require every single employee to email this person twice a day every day as we never start exactly at the scheduled shift time or get out exactly at the end of a shift. We are required to perform work activities in order to be ready to open and close our places of work every day. We are scheduled for our shifts to end at the same time the building is supposed to close so there is at least 5 minutes of extra work spent doing closing procedures and locking up. My question is-is it legal for the system to log us in and out at the scheduled shift times instead of when we actually arrive and depart from work and also is their solution of having us email every instance this happens OK? I thought it was the employers responsibility to keep accurate records of time worked?

What you described occurs the same the world over and is the accepted norm.
You are required to be at you allocated work station by a specific time for operations to begin.

First, the legalities of this vary depending on where you are located. But it certainly is a common occurrence. Especially the clock in. When employees clock in do they immediately go to their station and start working? Generally, an employee clocks in then takes a couple of minutes to get to their work station and start working.

Similarly, at the end of the shift, they stop working, put themselves together and then clock out as they leave the building.

When I originally wrote our timeclock software, I built in the same provision. As long as the worker clocked in or out within 6 minutes of their scheduled time, it defaulted to the scheduled time. More than 6 minutes and it recorded the actual time.

This is normal, You must clock in before the start time and clock out, after the quit time. This can be a minute to 5 or 6 minutes depending on time to the clock, and so on. This is the normal.

As someone who has at times in the last 37 years had to clock in and out at serveral different employers... You don't get paid from the time clock, you get paid by your schedule... you however may be docked pay based on the time clock for late clock in or early clock out.