Electrical panel grounding
From the International Association of Electrical Inspectors web site here:

If the metal water piping is not a grounding electrode, the connection of the bonding jumper in accordance with 250.104(A) does not have be located within the first 1.52 (5 ft) of the water piping system entry to the building or structure.

From my research, this was an old requirement (2005?) when the water pipe was used as the primary grounding electrode. It has since been deleted and does not appear in the 2017 NEC. Article 250.52(A)(1)
A ground rod (or two) is now required as the primary grounding electrode in most jurisdictions since someone could replace the copper piping with PVC in the future.[Edit: I just wanted to add that the Ufer ground (reinforcing rod in the poured concrete footing) is quickly replacing ground rods in new construction.]
However, if you do have a metal water piping system in contact with the soil for more than 10 feet it is still required to be bonded, although the National Electrical Code does not specify where.

250.104 Bonding of Piping Systems and Exposed Structural Metal.
(A) Metal Water Piping.  The metal water piping system shall be bonded as required in (A)(1), (A)(2), or (A)(3) of this section.
(1) General.  Metal water piping system(s) installed in or attached to a building or structure shall be bonded to any of the following: (1) Service equipment enclosure (2) Grounded conductor at the service (3) Grounding electrode conductor if of sufficient size (4) One or more grounding electrodes used, if the grounding electrode conductor or bonding jumper to the grounding electrode is of sufficient size
The bonding jumper(s) shall be installed in accordance with 250.64(A), 250.64(B), and 250.64(E). The points of attach‐ ment of the bonding jumper(s) shall be accessible. The bonding jumper(s) shall be sized in accordance with Table 250.102(C)(1) except as permitted in 250.104(A)(2) and 250.104(A)(3).

Summary, if it is NOT the primary grounding electrode, the metal water pipe is not required to be bonded within 5 feet, it is just required to be bonded.
I agree with Tester101 though you are pretty much at the mercy of the inspector unless you want to file a formal objection.

Also, for a washing machine in an unfinished basement near the laundry sink need a gfci? It is plugged into a single plug outlet.

ALL receptacles in the unfinished part of a basement and laundry areas are required to be protected by GFCI.
From the 2017 NEC

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 (E). The ground-fault circuit interrupter shall be installed in a readily accessible location.
(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.
(5) Unfinished portions or areas of the basement not inten‐ ded as habitable rooms
(10) Laundry areas

Good luck!