To answer your question it's nearly impossible to tell the difference between 36 and 37 exhibits that have the same players on them.
The only real way i can tell (and it's not 100%) is the color of each year is a little bit different. The problem is that 70 plus years of wear and fading make many look the same. I have a set of each year and if you lay them all out next to each other you can kinda see a difference between each year. The 36 have a blueish tint where as the 37 are closer to green/grey tint but its very hard to tell.
Here are two examples (first set its pretty easy to see the difference, second set both are faded and its much harder to tell if at all)-
