The North Country National ScenicTrail goes through some remote areas. Plan ahead prior to hiking. Parts of the trail go through designated wilderness areas. Know what rules govern hiking and camping in wilderness areas prior to your visit. Go to Wilderness.net for more information.
One of the best practices you can follow for your safety is to never hike alone.. Always let someone know where you are going and the date/time that you are expected to return. Develop a plan to check in with them before, during and after your hike. Plan hikes that match your level of physical fitness.
Safety issues to be aware of while hiking on the trail include ticks, poisonous plants, wildlife, and hunting (which is prevalent in many areas so prepare accordingly). You will be sharing the trail with other people. Unfortunately, not all can be trusted so use caution and common sense. Respect others with whom you share the trail.
For more information about safety, visit the North Country Trail Association's page on safety