I was reading How does the Hogwarts Headmaster know whom to invite to school? and it got me thinking, how can wizards and witches tell if a person they are dealing with is a muggle?
The answer is "they can't", absent visual cues (dress code, having a wand, living in Wizarding area etc...).
If you recall, Neville's family didn't even think he was a wizard till he got accidentally dropped out the window and bounced.
Aside from Harry and probably some teachers, nobody knows that Filch is a squib.
Now, considering that there's a special quill that records every wizard being born (for Hogwarts), that's plainly NOT a magically impossible task. But somehow, nobody ever displays any ability to clearly do so aside from said Quill as well as a Sorting Hat (who is telepathic).