Generally speaking the biggest flaws would be uneven honing pressure, not being able to keep the razor flat or having a stroke that leaves part of the blade with less honing action than other spots. In general: inconsistency in the various aspects of honing.
Changing to a different stroke (like making circles) may remove some of the symptoms in that case.
However, the magic is not in making circles, but in the fact that the circles make you lose one kind of inconsistency.