Can you keep a dolphin (mahi-mahi) in North Carolina?

No minimum size. The real cap is often the trip limit, not the per-person one: 10 a day per angler or 54 per vessel per trip, whichever is less. On head boats the limit is a flat 10 per person per day, and the recreational bag may not be sold from a vessel operating as a charter or head boat.

NC DMF source page

What we left out on purpose

• Cobia and the whole snapper, grouper, porgy, triggerfish, jack, tilefish, grunt, spadefish, wrasse and sea bass complex are set by DMF proclamation rather than by this table. Only cobia is carried here, and it is carried as unsettled; the complex is left out entirely rather than reproduced in part.
• Tuna (bluefin, bigeye and yellowfin) and the billfish group (blue marlin, white marlin, sailfish) are left out. DMF's own footnote for these species reads 'For seasons, bag limits, size limits or closures... contact NMFS Highly Migratory Species Division' — the same defer-to-federal marker as sharks and the snapper/grouper complex — and the table itself is incomplete for tuna (a size for bigeye and yellowfin, a bag for yellowfin only, nothing at all for bluefin). Wahoo, dolphin and spiny dogfish do not carry that marker and are published normally.
• The table prints the spotted seatrout allowance as "1 greater than 26' TL" — a foot mark where an inch mark belongs. It is read here as 26 inches, which is what every other figure in the row implies, but the typo is in the agency source.
• Bluefish shows the clearest gap between table and footnote: 5 a day in the row, 3 a day for private anglers in footnote (M). The 3 is published here. Anyone fishing from a charter or head boat gets the 5.
• American shad, hickory shad and sharks are set by proclamation and are not carried. Tarpon, alewife and blueback herring are unlawful to possess and are left out rather than listed as a zero.
• Shellfish and crustaceans — blue crab, stone crab, spiny lobster, hard clam, oyster, bay scallop, conch, mussels, shrimp — are a second table with their own measurements and closures. None of it is carried here; this silo is finfish.
• The table itself carries the disclaimer that it "IS FOR GENERAL INFORMATIONAL PURPOSES AND HAS NO LEGAL FORCE OR EFFECT" and that rules are subject to change. The binding text is the rule and the current proclamation.