I think I found a fix so that the connection issue can be prevented completely, as long as the cart pins are clean. Basically what it is is the pcb inside the adapters case has slack. The post from the shell in the center that hold the adapter pcb in place are a tad thinner then the actual pcb through holes. Due to that as you insert a cart on it, the adapter pcb inside the shell can be slightly forced downward, making the connectors on one side of the Nes cart slightly lose connection.
Basically on a Nes game, any given one, one side of the connectors has less length then the other side. The shorter connection side loses connection slightly due to that slack and the adapter pcb shifting position.
My fix for this was taking some strips of clear then plastic and folding them to the correct thickness to make them into wedges, then sticking them at specific spots inside the shell so that they will prevent the adapter pcb from shifting postion down low anymore. I used dabs of hot glue to keep the wedges in place. All in all it works rather well.


EDIT: Yeah this fix did exactly what I expected it to do. No more slack, so the adapter pcb no longer shifts postion. So now I don't have to dick around with sliding the thing left or right on the Nes carts to try to make it connect better on some of my carts. Now everything works fine right from the get go, on the first try.