I think nothing is wrong with Zeno's design of the racing, although someone may argue that an infinitesimal time interval is physically impossible. With today's mathematics we often do calculus in this way never thinking about if it is physically possible and no error caused by this way of thinking; then how can we accuse Zeno? That is not the point of the paradox. The point is the second part: the wrong interpretation of the result.
All proposed solutions seem to argue the first part while nothing wrong with it. This is the reason I propose the phrase as below:
Zeno's trick is in fact to freeze time causing the racing stopped. Achilles is able to overtake the tortoise but not able to do so in this specially designed racing. Therefore, Achilles cannot overtake the tortoise in THIS racing does not mean Achilles is unable to overtake the tortoise.
Xuetao Zhang, Gothenburg, Sweden