Yes you can take
Mobic with a narcotic pain med.
Mobic is a NSAID, and has the same risks as other NSAIDS.
In high doses it can cause some kidney issues, the vicodin has tylenol in it and can cause some liver issues in high doses.
But they are safe to take together. Typically what you want to watch for is multiple NSAIDS, or Multiple meds with tylenol.