Good question. bump.

Are there 2 GFCI breakers in the panel? Was new wiring used all the way back to the panel? Are the receptacles 2 or 3 prong type? Does the old cable have a grounding wire? How old was the old wiring? The NEC does not require a GFCI for the under the sink dishwasher receptacle in most states (yet). When will the inspector be there?

in michigan, all outlets near any water source must be GFI or it will not pass inspection.

If you remove a receptacle in a kitchen that serves the counter top, it must be replaced by a GFCI protected receptacle. The GFCI can be a breaker in the panel. 406.3(D)(2) requires GFCI protected receptacles where replacements are made at receptacle outlets that are required to be so protected elsewhere in the NEC. These receptacles, using existing boxes and wire without a grounding conductor, can be installed without attaching a wire to the green ground screw on the receptacle. The GFCI will still protect people.
The fine print note found in 406.3- FPN No. 2: For extensions of existing branch circuits, see 250.130.

It is important to note that an outlet is any box for using power including lights. GFCI codes generally only refer to receptacles (the things you plug cords into)

Once you gut the kitchen, the new outlets become an extension and not a replacement. These new outlets must conform to the current NEC including the new wire with a grounding conductor and the green screw on the receptacle attached to the grounding conductor. When it is difficult to start a new circuit from all the way back to the panel, NEC 250.130(c) provides a way to connect the new grounding conductor to the same grounding 'system' as the panel by an alternate route. This procedure is hard for many electricians to understand AND it can be inadvertently undone by future remodels.
Massachusetts has rejected this part of the NEC.
250.130(C) Nongrounding Receptacle Replacement or Branch Circuit Extensions. The equipment grounding conductor of a grounding-type receptacle or a branch-circuit extension shall be permitted to be connected to any of the following:
(1) Any accessible point on the grounding electrode system as described in 250.50
(2) Any accessible point on the grounding electrode conductor
(3) The equipment grounding terminal bar within the enclosure where the branch circuit for the receptacle or branch circuit originates
(4) For grounded systems, the grounded service conductor within the service equipment enclosure
(5) For ungrounded systems, the grounding terminal bar within the service equipment enclosure
FPN: See 406.3(D) for the use of a ground-fault circuit-interrupting type of receptacle. (this note does not apply to new receptacles, just replacement of existing ones)
This is where the confusion comes in. If you do not have two GFCI breakers in the panel for the kitchen, or two GFCI receptacles somewhere in the kitchen after pulling out the old receptacles, your kitchen does not meet Massachusetts code. Further, if you do not have new 12-2 NMB with ground wire (it has a yellow sheathing) going all the way back to the panel, your kitchen does not meet Massachusetts code.
There is no exception in the NEC that says if it is too much trouble to comply with one part of the code, that not putting in the required GFCI protection will make it right. Two wrongs do not make a right. Eliminating 250.130(c) did not negate the remainder of the code book that it was related to.

In general, the only receptacles in the kitchen that need GFCI protection are the ones designed to serve the counter. That means any receptacle 20" above the counter to 12" below the counter and not inside an upper or lower cabinet.
The 2014 NEC now requires a GFCI for dishwashers.
Article 210.8(D) GFCI for Kitchen Dishwasher Branch Circuit.
GFCI protection shall be provided for outlets that supply dishwashers installed in dwelling units. This includes receptacles and hardwired (All GFCI’s must be readily accessible).
This usually only effects all work that applied for a permit after Jan.1st 2014 (in the case of Massachusetts) other states may not have adopted this code yet. (Michigan, for example, adopted by reference the 2011 edition of the NEC effective on July 1, 2013 and probably won't have the dishwasher requirement for a long time.) It doesn't necessarily apply to work already in progress at that time.

A dedicated receptacle for a refrigerator in a kitchen, behind the refrigerator, does not have to be GFCI protected.(yet) They do need to be GFCI protected in garages and basements.

Here are Massachusetts amendments to the NEC.
http://www.mass.gov/eopss/docs/dfs/board-meetings/2013-9-7-massachusetts-2014-code.pdf

Some more light reading:

210.8 Ground-Fault Circuit-Interrupter Protection for
Personnel. Ground-fault circuit-interrupter protection for personnel shall be provided as required in 210.8(A) through
(C). The ground-fault circuit-interrupter shall be installed in a readily accessible location.
Informational Note: See 215.9 for ground-fault circuit interrupter protection for personnel on feeders.
(A) Dwelling Units. All 125-volt, single-phase, 15- and 20-ampere receptacles installed in the locations specified in 210.8(A)(1) through (10) shall have ground-fault circuit interrupter protection for personnel.
(1) Bathrooms
(2) Garages, and also accessory buildings that have a floor located at or below grade level not intended as habitable rooms and limited to storage areas, work areas, and areas of similar use.
(3) Outdoors
Exception to (3): Receptacles that are not readily accessible and are supplied by a branch circuit dedicated to electric snow-melting, deicing, or pipeline and vessel heating equipment shall be permitted to be installed in accordance with 426.28 or 427.22, as applicable.
(4) Crawl spaces — at or below grade level
(5) Unfinished basements — for purposes of this section, unfinished basements are defined as portions or areasof the basement not intended as habitable rooms and limited to storage areas, work areas, and the like
Exception to (5): A receptacle supplying only a permanently
installed fire alarm or burglar alarm system shall not be required to have ground-fault circuit-interrupter protection.
Informational Note: See 760.41(B) and 760.121(B) for power supply requirements for fire alarm systems.
Receptacles installed under the exception to 210.8(A)(5) shall not be considered as meeting the requirements of 210.52(G)
(6) Kitchens — where the receptacles are installed to serve the countertop surfaces
(7) Sinks — where receptacles are installed within 1.8 m (6 ft) of the outside edge of the sink
(8) Boathouses
(9) Bathtubs or shower stalls — where receptacles are installed within 1.8 m (6 ft) of the outside edge of the bathtub or shower stall
(10) Laundry areas

Don't forget AFCI requirements.

210.12 Arc-Fault Circuit-Interrupter Protection. Arcfault circuit-interrupter protection shall be provided as required in 210.12(A) (B), and (C). The arc-fault circuit interrupter shall be installed in a readily accessible location.
(A) Dwelling Units. All 120-volt, single-phase, 15- and 20-ampere branch circuits supplying outlets or devices installed in dwelling unit kitchens, family rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms sunrooms, recreation rooms, closets, hallways, laundry areas or similar rooms or areas shall be protected by any of the means described in 210.12(A)(1) through (6):

Holy cow, Fred!!

There WILL be a test! :D

I would surely fail!!

And that was the simplest answer I could come up with, without more specific information from @north. I may have even left some out. Hope it is not in vain as the OP has not responded back in 24 hours :-/
It is very important tor the OP to answer questions related to their inquiry if they want a real answer.

When I "bumped" it yesterday, I considered typing in "FRED????" instead. LOL!
You provided an amazing response here. I'm assuming you didn't do that from a little hand held device? PS...they are missing you in the cookie jar.

Perhaps they will come back, answer your questions and provide a photo also.

Call your building inspector and ask him to come to the site and get his opinion. The buck stops with the inspector. I am in MA.
P S You hold the checkbook.

Sorry folks. My internet is down more than up. I will read all this and get back to you. Thanks!