Here are the oddities. First, it's not a Mustang. The picture is of the final approved design of the Ford T-5 project taken in 1963. All that remained was a name, and "Cougar" was the top choice right up until the last minute. Other name considered were: Special Falcon; Torino; Turino; Colt; Bronco; Maverick; Pinto; Monte Carlo; and H. Ford's favorites - Thunderbird II and T-Bird II.
So technically, the picture has no defects and nothing wrong. You are all correct in what you state would be incorrect for a 1964 1/2 Mustang: the Cougar in the corral; the lack of horizontal grill bars; a shiny (chrome?) grill; no bumper guards (the picture of the rear quarter has none either); no side emblem; no scoop trim; no rocker trim; and the final non-compliant item - there's a tab under the lower grill horizontal piece that attaches to the vertical hood latch support that should be painted semigloss black, eg, blacked out, on all 64 to 66 Mustangs with a light exterior color. There are many concours grade Mustangs that missed a perfect score because of this tab not being painted. Also in the picture from the rear, the differential has a flat bottom look, therefore I think that this was a I-6 equipped car.