As a project leader your job is to monitor progress against the project plan. But you don't have to do this alone. Use buddy checks to verify that tasks are done properly. When someone completes an activity, have another team member look at the results. This shouldn't be an in-depth analysis, just a quick check to confirm that the person didn't overlook or misunderstand anything. The ideal reviewer is someone who will use the results of the task. Just make clear that this is not a performance appraisal. It's one team member looking out for another.