I think it will really come down to the audit functions of the timesheet supplier. There needs to be good workflows in place that are controlled by
HR (or payroll if no
HR function) by way of keeping an org structure up to date so the correct manager is approving their employees only.
If there is any queries over who actually approved it, the system must be able to show the flow of the timesheet from the employee, to the manager for approval and then onto the payroll system for processing. (this should also come with a date stamp for a bit better audit ability)
If you look at your current processes, you'll probably find an improvement over the paper timesheets if your company is currently like most I've encountered. The employee gives the form to the manager, the manager signs it and gives it back to the employee to take to the payroll dept. The managers rarely look at (or understand) any payroll end reports they receive and so there is potential for the employee to add extra hours to the timesheet after the manager has signed it. Electronic timesheets remove this ability.
Also keep in mind contingencies for the manager being on planned / unplanned leave. It's not good enough in this day and age for employees to miss out on getting paid on time because their manager is simply on leave.