But it's not just the doctors who can tell if someone's autistic. Autistic people, and people who know autistic people (such as family members) can often spot autism - not necessarily with enough accuracy for an official diagnosis, but this still shapes their interactions with these people in various ways.
A similar thing happens among gay people. Gay people, and to a lesser extent straight allies, often have a finely attuned 'gaydar' - a sense of whether or not someone else is gay. This depends partly on unintentional cues, similar to the cues diagnosticians try to observe, but also partly on intentional signals that gay people use to find each other.
Autistic people aren't as common as gay people, and have a much less developed community, but we also use cues to tell each other from neurotypicals. Jim Sinclair, in his article Alien Contact, describes the use of both sorts of signals:
"The women [mother & daughter] were talking quietly to each other. I couldn't make out the younger one's words. But I could hear their rhythms and their tones, and I knew them, and I knew her for one of my people."
[he also describes specific behaviors, such as repetitive speech, that signal this to him]
"And so, standing there in the aisle, knowing they were looking at me, I let my body begin to rock, let my hands begin to flap. Not too much. Only a little. I'm sure the mother never noticed."
Personally, in my volunteer work, I can often guess what disability the child I'm assigned to has been diagnosed with (or should be). Certainly, I can spot the autistic kids. When I work with an autistic kid, especially, I let myself act more autistic, hoping that they'll pick up on that and recognize me as one of their kind. And I get the sense that many of them do, particularly the more severely autistic kids (who, ironically, seem to be more in tune with nonverbal cues), because they often relate to me differently. It's subtle - somewhat greater interest in me, more initiation of interaction, more response to my own interaction. Sometimes I can't even see it until I watch them with someone else. Sometimes I don't see it at all, but someone else does. But the thing is that different mannerisms and nonverbal communication aren't just something that diagnosticians use to find us. We also use them to find each other.