How can I review some types of tasks before they are marked complete?

You can create an additional stage called 'Review', and make sure that task owners move the task to the 'Review' status after they complete the task and log time. They can assign the task to the staff member who will review their work. The new owner will get a notification and can complete the review, and move the Task to 'Completed'. Or move the Task back and reassign to the same staff member, after adding comments on the Task.