The Wesen obviously have a physical change they can display to one another, yet a Grimm has no change. Frequently when Nick confronts a Wesen they immediately know him as a Grimm, but how?
This was finally answered in season three episode seventeen (about 12 minutes in), Synchronicity:
Monroe: It's your eyes.
Nick: My eyes?
Rosalee: It's how we know you're a Grimm after we woge.
Monroe: They turn black.
Rosalee: Not exactly black.
Monroe: No, you're right, actually. Black's too weak a word. It's more like infinite darkness. And we see ourselves reflected in that darkness. We see our true wesen nature.
We have been given a hint in 3x09, Red Menace. It's a minor part of an interrogation, so I'm not going to bother spoilering it:
The Wesen-of-the-week is surprised that Nick saw earlier what he is. So, sitting in the interrogation chair, he pauses a moment, shifts fully, then recognizes Nick as a Grimm. He however doesn't recognize that Hank is a plain human, nor that Captain Renard is a Royal/Hexenbiest hybrid.
Looking back, this has been very consistent: The Wesen shifts out of surprise or fear almost immediately after meeting Nick, then recognizes him as a Grimm. Normally this happens so quickly we can play it off as coincidence, but not this time. He shifted in order to look at Nick with his Wesen senses and confirm what he suspected.
While we can't yet say exactly what they see or sense, this is basically a reversal of the Wesen shifting: Something only Wesen can see/sense, as opposed to something only Grimms can see.
Keeping in mind that all creatures of the Grimm world are those based on animals and stories, you'd have to look for a "grimm" story. What comes up is the grimm and simmilarly, the black shuck. Both are recorded to be large, black (what color is Nick's hair? What color has all the Grimms we've seen so far wear all the time? think about it...), spectral dogs with flaming eyes (flaming eyes as in nothing but hell red. No sclera (whites), no pupils, just red). The difference? "Grimms" are recorded as violent killing machines that roam the country side at night. "Black Shucks" are kind dogs that gaurd graveyards, churches, and travellers. My theory is that the humans (who grimms help and protect) recorded Nick's species as Shucks and the Wesen (who grimms hunt and slaughter) recorded them as Grimms, though they are one and the same. I think what happens with Nick is that he gets the whole flameing eyes thing when he sees Wessen but can turn into the all out spectral dog once he learns how. This also contributes to the reason why Grimms aren't considered Wesen. Unlike wesen, who can go half man-half beast, full human, or full beast Grimms can only be in human form or beast form.