Wiring requirement for small kitchen
Looking at the actual code...

National Electrical Code 2014
Chapter 2 Wiring and Protection
Article 210 Branch Circuits
210.11 Branch Circuits Required.
(C) Dwelling Units.
(1) Small-Appliance Branch Circuits. In addition to the number of branch circuits required by other parts of this section, two or more 20-ampere small-appliance branch circuits shall be provided for all receptacle outlets specified by 210.52(B)
210.52 Dwelling Unit Receptacle Outlets.
(B) Small Appliances.
(1) Receptacle Outlets Served. In the kitchen, pantry, breakfast room, dining room, or similar area of a dwelling unit, the two or more 20-ampere small-appliance branch circuits required by 210.11(C)(1) shall serve all wall and floor receptacle outlets covered by 210.52(A), all countertop outlets covered by 210.52(C), and receptacle outlets for refrigeration equipment.
(3) Kitchen Receptacle Requirements. Receptacles installed in a kitchen to serve countertop surfaces shall be supplied by not fewer than two small-appliance branch circuits, either or both of which shall also be permitted to supply receptacle outlets in the same kitchen and in other rooms specified in 210.52(B)(1). Additional small appliance branch circuits shall be permitted to supply receptacle outlets in the kitchen and other rooms specified in 210.52(B)(1). No small-appliance branch circuit shall serve more than one kitchen.

The receptacles supplying the countertop, must be supplied by at least two 20 ampere circuits.  However, these two circuits can also supply receptacles in a &quot;pantry, breakfast room, dining room, or similar area of a dwelling unit&quot;, as well as &quot;receptacle outlets for refrigeration equipment&quot;. One of the more common ways to meet this code, is by splitting the duplex receptacles. One circuit powers the top outlet of the receptacle, while the other powers the bottom outlet. Another option is to supply the countertop receptacles with one circuit, and the refrigerator with a separate circuit.
As for the receptacle in the kitchen, supplied by the living room circuit. While this is likely not a violation. This receptacle does not count towards the two 20 ampere small appliance circuits required in the kitchen.