gear down during takeoff for extended period of time
It's usually for one of two reasons: 

Brake temps are displayed in the cockpit and if the temps were elevated from a lot of, or excessive, brake use during taxiing, the capt may delay retraction until the indications come down, mainly to avoid gear bay overheat indications. This will be more common on airplanes that have more idle thrust than necessary to roll at normal taxi speed, which can cause a tendency to ride the brakes.  CRJ200s, which can get going pretty fast on idle thrust with both engines running, are really bad for this.

Also in winter on a departure from a slushy runway, retraction may be delayed to try to blow off as much slush as possible since once the slush freezes, it can immobilize the wheels, preventing normal spinup on the next landing (if it's still cold at destination).