This question already has an answer here:
Is has been established that Logan takes place in 2029.
And, as can be seen from the trailers 1 and 2, it takes place in desert terrain in Oklahoma, Texas, and Mexico. So most things are old and dusty. But, for example, the cars and objects in the gas station store don't appear to have been modified to appear to be from our future.
Besides the obviously sci-fi elements (cybernetic mutants and their weapons, for example, which in the X-Men universe are not necessarily futuristic) is there anything else that would indicate that this is 12 years into the future?
Edit: Follow on question: What are the non-contemporaneous items or design choices in Logan?