What are the dangers of AI applications for nuclear industry? I've found this old scientific paper from 1988 about introduction of AI into nuclear power fields.

Were or still are there any dangers by application of such algorithm? Are nuclear power plants or human life in risk if the algorithm will fail?

Especially applications to the core, like cooling systems and other components which can be affected in negative way.
Any technology in the nuclear industry represents variance--it may be an improvement in safety or efficiency, or it may contain some unseen defect that allows a catastrophe to happen.

But the simple possibility of harm isn't enough to swing the decision one way or the other. The application of AI methods--whether to the real-time control of plant variables, or the early detection of problems, or to the design of plants and their components--seems likely to be as beneficial as in other realms.

For example, check out the publication list of a lab active in this area. Their paper I'm most familiar with is one in which they build a fault detector paired with a fault library classifier, so that the operators can be alerted not just that something is abnormal but what fault has probably occurred. This is done in such a way that standardized plants (such as, say, the French nuclear system) can share records with each other, meaning that any plant has the experience of every plant at their fingertips.