What are some of the most important things to keep in mind, when making great falafels?
Some points in addition to rackandboneman's excellent advice:


Use soaked dried chickpeas, and not canned or cooked chickpeas.  This eliminates the need for flour or other binders, as well as tasting better.
Let the batter rest for at least 20 min.
Remember to season the batter with cumin, garlic, and herbs.
The balls should be formed and dropped directly into the hot oil.
The oil needs to be between 360F and 380F (185 and 195C).
Falafel balls should be eaten hot from the fryer, and not reheated.


The above is based on the advice of a friend of mine who used to work at Sunrise Deli, who had the best falafel balls in San Francisco at the time.  It is generally supported by Serious Eats' recipe and advice.