Question: Is there a way I can make the timesheet screen just show the current pay period? 


The dates that are shown in the timesheet window default from the Payroll's up and coming pay period for the person selected. You can change the start and end dates at the top of the window, however, any timesheet that has not been processed through payroll, in the past, will always show in the timesheet window so they are not forgotten or accidentally sent to payroll and processed.