Well, this is where we really get to the "low effort/high impact" philosophy: The bots don't look for circles. That's too hard/I'm too lazy. So they do something much easier, and generally better: They look for a net change in heading equal to 4*360 degrees.

  (defn curviness
    "Computes the total curvature of a sequence of headings."
    ^double [headings]
    (Math/abs
     ^double (reduce (fn [^double sum [^double a ^double b]]
                       (let [d (heading-diff a b)]
                         (if (spurious-heading-diff d)
                           sum
                           (+ sum d))))
                     0.0
                     (partition 2 1 headings))))

This is what allows the bots to find interesting activities I didn't think of ahead of time.

While the traffic pattern is indeed rectangular, the "flying in circles" may come off as almost a joke to people involved in flight training (at least it did to me as a student) because one of the maneuvers you are required to learn/be able to demonstrate is flying a perfect circle. So there are, almost comically literally, a lot of student pilots out there going around and around in circles. Also rectangles and S-curves and figure-eights, and I wonder if you could do a little filtering to pick up people practicing their stalls, but I'm not sure if the temporal resolution on ADS-B altitude is enough to get that.

Usually in urban areas there's a more or less formal designated practice area where people are doing these things, intentionally not near the airport, but you could filter out small aircraft in those areas if it was really an issue.

True, I didn't think of that but things like "hold a 30 degree turn for a certain amount of time" could indeed result in a circular flying path. You are right.