The main problem that has been identified is of overdiagnosis. This means that growths and cancers may be identified which are harmless, but which get treated anyway - with whatever risks the treatment itself may involve - although if they were left alone, there would have been no problem. A recent study for the NHS worked out that if you took 10,000 women aged 50 and over, receiving screening treatment, in current conditions, over 20 years about 680 cancers would be diagnosed and of these 120 would be overdiagnosed. This level of detection would mean that 43 deaths would be prevented, so if you look at it like that, the rate of overdiagnosis is three times the rate of prevention.
However, overdiagnosis is not in itself harmful at all - it's only the subsequent treatment that could possibly be harmful, and may well not be so at all. The fact is that overdiagnosis is bound to happen, because in the early stages you can't often tell if a cancer will be harmful or not, but waiting until you are sure isn't a good idea either.