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Op-amp in сurrent-sensing

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In the book of "The Art of Electronics", Chapter 7, on page 422 one can see the following schematic diagram and read this commentary:
"Even though one side of R5 is connected to ground, it would be unwise to use a single-ended amplifier, since connection resistances of a milliohm would contribute 10% error! A differential amplifier is obviously required, but it need not have particularly good CMRR, since only very small common-mode signals are expected."

So my question is: Which connections' resistances(segments of wiring) are exactly meant by authors?
Thanks in advance to all who could be of any help to understand this.

post-62253-14279144320537_thumb.jpg

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