If some air accidentally entered the eudiometer when it was transferred to the tall graduated cylinder, then the value of R would increase. This is because in my manipulated gas law equation, R=PVnT, volume is on top, in which if it's value increases, then the value of R will also increase. And because volume is directly correlated by the how much gas is in the eudiometer, the more gas in the eudiometer, the bigger the volume and R value.
If some of the magnesium ribbon was left over after the reaction, then the value of R would increase. This is because having extra magnesium leftover means that it came in excess and there was more magnesium to react