How can I detect and highlight pixels that fall outside sRGB in an image?

The Foundry Nuke or Blackmagic Design Fusion perform operations with floating point numbers which allow you to implement that type of tests. It essentially boils down to convert your image from DCI-P3 to sRGB colourspace and check for any negative numbers in the output image/array. Here is an example in The Foundry Nuke:

This is the above node tree that you can copy-paste into the application:

set cut_paste_input [stack 0]
version 10.5 v2
Read {
inputs 0
file /Users/kelsolaar/Downloads/Italy-P3.jpg
format "600 400 0 0 600 400 1 "
origset true
name Read1
selected true
xpos -50
ypos 11
}
set N30e152e0 [stack 0]
push $N30e152e0
Colorspace {
illuminant_in DCI-P3
primary_in DCI-P3
bradford_matrix true
name Colorspace1
selected true
xpos -50
ypos 91
}
Expression {
expr0 "r < 0 ? 1 : 0"
expr1 "g < 0 ? 1 : 0"
expr2 "b < 0 ? 1 : 0"
name Expression1
selected true
xpos -50
ypos 115
}
Viewer {
inputs 2
frame_range 1-100
input_number 1
name Viewer1
selected true
xpos -50
ypos 139
}

If you are comfortable with Python, you can also use Colour as follows:

import numpy as np

import colour
import colour.plotting

DCI_P3 = colour.read_image('/Users/kelsolaar/Downloads/Italy-P3.jpg')

sRGB = colour.RGB_to_RGB(DCI_P3, colour.DCI_P3_COLOURSPACE, colour.sRGB_COLOURSPACE)

colour.plotting.image_plot(np.where(sRGB < 0, 1.0, 0.0), 'sRGB - Out of Gamut')

The source image is available at this url: https://webkit.org/blog-files/color-gamut/Italy-P3.jpg

As mentioned by @doug in the comments below, and given that the original post is about images in general and also specific to iPhone images, it is important to note that colours with high chroma and luminance might also overflow the [0-255] range. Those values need to be accounted for if you encode your images in an low dynamic range container, e.g. JPEG, PNG or any integer based image format.