Pulmonary Embolism Support Group
By far the most common form of pulmonary embolism is a thromboembolism, which occurs when a blood clot, generally a venous thrombus, becomes dislodged from its site of formation and embolizes to the arterial blood supply of one of the lungs. Symptoms may include difficulty breathing, pain during breathing, and more rarely circulatory instability and death.
I suspect it's 'not typical' in the sense that it's a rare complication, but 'typical' in the sense that it's a known complication.
We did successfully avoid pneumonia, but I battled pleurisy a lot for at least the first year after PE. (I mention both things because I'm not really sure which you mean when you say fluid on the lung.) But the pleurisy was also considered by my doctors as an almost expected complication.