Problem: Error reported while activating Samsung Galaxy Watch, touch device info on the error message screen in order to see the error code then follow below steps to resolve the issue.
Error Code 4001: Grant Permission
Grant Phone permissions to the Carrier Login Engine app to access the Phone functions.
Step 1: Go to Apps > Settings > Apps > More Options menu > Touch Show system apps > Permissions.
Step 2: Touch the slider to turn the permission on.
Step 3: With the SIM inserted, reboot the phone and make sure connected to mobile network.
Error Code 4002: Update Software
Check for updates for both phone and Galaxy Wearable app.
Step 1: Go to Apps > Play Store > Menu > My apps & games.
Step 2: Touch UPDATE ALL to update all apps.
Note
Galaxy watch is currently supported by AT&T, Sprint, T-Mobile and Verizon.
Source
Samsung Troubleshooting Guide: Galaxy Watch Activation Errors