In an experiment to find the resistance of an ohmic conductor, current I is plotted against potential difference V. The plotted points lie on both sides of the best fit straight line. Which feature of the graph is evidence that random errors are present?

Random errors vary in size and in sign from one reading to the next, so each plotted point is pushed off the true line by a different, unpredictable amount. That is exactly what scatter about the best fit line looks like. A line that misses the origin is a systematic effect, since it shifts every reading the same way, and a steadily rising straight graph is just the ohmic behaviour the experiment set out to test.