If you have a chance to speak to somebody or even hear them talking to somebody else then look out for some of these signs.
From my experience, the more a person makes snap judgments (I know I'm talking about judging people, but I'm referring to people actually saying this aloud) going off of very little information then the less intelligent they tend to be. Also, things tend to be one extreme or the other. "That's good." "That's bad." "He's a douche." etc. I have a theory about the people who apply extreme labels to everything ("It was the BEST thing in the world." "She was PISSED." "I'm sooo STARVING." "The movie was the absolute worst thing I've ever seen."). I think it makes for better gossip and for making inconsequential things seem interesting, since they spend so much time talking about surface level, mundane things they need to spice it up somehow. That's another topic, but I think that if you hear someone use a lot of extreme adjectives and over exaggerations then they're probably more likely to not value truth and are only interested in gossip and surface level conversations.
Curiosity is a mark of intelligence, so if a person shows this then I tend to give them a little bit of credit. I see this as related in some way to snap judgments. The more curious a person then the less likely they are to immediately apply labels to things because their mind is busy, or they realize that it's not black and white.
Rude, inconsiderate, or careless people tend to be less intelligent. This is tied to awareness or lack thereof, as somebody else has already pointed out. Rude people are less self-aware, or if they are aware and are still rude then they're just not thinkers.
If they seem disingenuous, or they seem entirely too conscious of their movements and mannerisms then I count that as a mark of less intelligence. There are of course exceptions, since I know some very smart people on the edge of the autistic spectrum who are very awkward, but I think in general the more obviously phony a person is then the duller they are mentally. People unconsciously pick up on phoniness to some degree and in return give off signals of distrust or skepticism, and the people who are unable to notice these signals that they're receiving are the ones who continue on being disingenuous, completely unaware that people know. There are of course smart people who present false selves, but if they're actually bold enough to do that then they're more likely to go under the radar because they're better at it.
The more I continue this list, the more I realize that a lot of it comes down to awareness. Dumber people are less self-aware and less considerate of others, so they will be louder, ruder, if they're disingenuous then it will be more noticeable. Their attention will be on surface qualities and surface issues, nothing deeper. Or if they do speak about something deeper, they merely spout conclusions since they're really just parroting what they've heard other people say. They will be more confident in announcing snap judgments.
Smarter people tend to show more consideration of people and things. They tend to be more genuine and have a better sense of awareness for themselves and the area around them. All of this is in general, and I can think of exceptions to all of these rules for certain times and places but I think this is a good generality of some of the differences when hearing people speak.