Production of nuclear weapons - radioactive materials used in this production have high health risks and release a small amount of pollution. Thanks to good current health-standards this release is not significant and is not a danger to us unless an accident occurs. Standards have not always been so high, however, as in Fernald, Ohio.
Decommissioning of nuclear weapons - the decommissioning of nuclear weapons causes slightly more radioactive pollution than in the production, however, the waste (alpha particles) is still of low risk and not dangerous unless ingested.
Mining of radioactive ore (uranium, phosphate etc.) - mining these involves crushing and processing of the radioactive ores and this generates radioactive waste which emits alpha particles. This waste is of low risk unless ingested.
Coal ash - it may come as a surprise that coal ash can be very dangerous. Some coal contains more radioactive material than usual and is often referred to as 'dirty' coal; when this is burnt the ash becomes more radioactive as the radioactive particles do not burn well. This level of radioactivity is less than in phosphate rocks, however, due to small amounts being released into the atmosphere and its ability to be inhaled, this ash is significantly more dangerous.
Medical waste - a number of radioactive isotopes are used in medicine, either for treatment or diagnostics. These can be left to decay over a short period after which they are able to be disposed of as normal waste.
Nuclear power plants - nuclear power plants under current standards produce little radioactive pollution due to safety precautions that must be adhered to. Accidents at these power plants can cause dangerously high radioactive pollution, such as in the case of Chernobyl, the most well-known and worst nuclear disaster in history and the more recent Fukushima, after the earthquake and tidal wave in Japan.