Can a fiberglass cast on your leg leave bruises and abrasions?

Yes, it most . Certainly can. (not what we want, but it does happen.).
Injury vs cast. Bruising often shows up in a delayed fashion after an injury or surgical procedure and is more likely related to this process than the cast itself.
Basically, yes. There may be times that swelling in the leg goes up or down and can cause bruising. Most times the bruising is caused from the original injury. Abrasions can often times come from the cast padding being taken out or the cast rubbing on the skin at the ends of the cast. Abrasions or scratches can at times come from the cast saw coming into contact with the skin during cast removal.
Maybe. Bruising usually not caused by a cast, more often the result of the injury of surgery that caused you to need a cast in the first place. If the fiberglass is sharp at the top or bottom of the cast in can cause abrasions.