Yep, if you’re literally dropping balls from a tower then firstly you’ve got to be very precise in dropping them at the same time. But also, it occurs to me, that if the lighter ball is too light then maybe it will get close to its terminal velocity? Or if the wind makes its path slightly curved it will also land later.
It shows how important experimental design is, or you might get an anticipated result for an unanticipated reason 
I agree with this quote from the article:
“The associated open science reform movement aims to rectify conditions that led to the crisis. This is done by promoting activities such as data sharing and public pre-registration of studies, and by advocating stricter editorial policies around statistical reporting including publishing replication studies and statistically non-significant results.”
Especially the part about advocating stricter editorial policies and addressing evidence of publication bias. I admit I didn’t read the whole article…
Yikes, now he’s getting angular acceleration of the spheres mixed in with the linear (on a slope) acceleration.
Frequently, “common knowledge” notes the obvious correlation between two factors - but is wrong in assigning causality.
Example: before science came up with germ theory, it was “common knowledge” that miasmas (bad smells) cause disease - therefore one tried to fight contagion by masking the foul smell with perfume-filled pomanders and posies of sweet-smelling flowers and herbs - could the custom of bringing flowers to the sick harken back to these dark origins?
It was science that eventually proved that by eliminating the common causes of foul smells and rampant disease, poor sanitation and hygiene, generally also more prevalent under slum conditions than amongst the affluent, could significantly curb the spread of disease.
Another example: The common cold
You feel cold, and a few hours later, you are running a fever and feel sick. You have “caught a cold” (Erkältung in German). However, this obvious correlation in most cases is not due to cold temperatures causing the disease, but your immune system reacting to a viral infection caused it to adjust your inner thermostat to achieve higher body temperature. The developing fever causes you to feel cold, independent on the external temperature. You can get the same effects of feeling cold, then getting a fever and feeling unhealthy by injecting a person with interferon gamma - A peptide released by virus-infected cells to alert the immune system that something is amiss.
In addition, in the colder (but not extremely cold) and wetter weather of the cold season, the causative viruses survive longer than in dry and hot weather, reinforcing the apparent correlation between cold temperature and the collection of viral infections called “a cold” in common language.
And if he were trying to determine precisely what the acceleration was, then that’s be a problem. But he was still at the stage of just determining that there was an acceleration. As long as all of his test masses were uniform solid spheres, no problem.
Though it’s probably a good thing that he didn’t use any cylinders, or rings, or hollow spheres, in addition to his cannonballs, because he (or anyone else of his time) didn’t have anywhere near the theoretical background to figure that one out.
It would also be an issue if he had guided different-sized but still uniform spheres down the angle using a trough in which the bottom of the spheres did not touch, because the spheres would sit in the trough at a different angle, resulting in more rotational acceleration for the smaller sphere and less linear acceleration.