Patella femoral syndrome can cause arthritis if left untreated for an extended period of time.
Arthritis, or osteoarthritis to be more specific, is an inflammation, irritation, and or degeneration of the articular surfaces and bone of a joint. It generally comes after many years of stress to a joints surfaces - for most it is caused by normal wear and tear, and may begin in a persons 50's, 60's, or 70's.
Any activity or condition that causes abnormal stress on the joint surfaces has the potential to end up causing arthritis later in life if the abnormal stresses last for long enough. So, PFS that is left untreated and continues for many years, especially coupled with sports activities, can lead to arthritis later in life.