Lets start with the premise:
Intelligence measures mental acuity, accuracy of recall, and the ability to reason (phb.177)
Wisdom reflects how attuned you are to the world around you and represents perceptiveness and intuition (phb.178)
So a wise character will pick up on things that a normal person might not, such as identifying the warning signs that something just doesn't feel right with a specific situation.
Now I don't have this ability, and most DM's struggle with giving enough clues or even creating a world where warning signs are something that can be picked up on at all.
A less intelligence character wouldn't know many facts, wouldn't learn from books, and wouldn't quickly put 2 an 2 together when confronted with a situation.
So you are left with a character who might spot all sorts of warning signs going into a situation, but not necessarily know what they mean.
What are some strategies to help roleplay such a character? Especially in a situation where every word a DM says will likely be taken as important by everyone around the table so won't stand out specifically to the person playing the character in question.
One source of inspiration has been Caduceus on Critical Role, but that seems to be the actual player picking up on things in order to make the wise comments, and I just don't pick up on the same things in real life.
Note: If it matters, the particular character in question has 6 INT, and currently 16 WIS.