Nuclear plant workers are inspected thoroughly enough for contamination, as seen by recent events in the state of Washington. A worker at a shuttered nuclear weapons plant was contaminated with plutonium, which triggered a federal investigation into the contamination source. Clearly, inspection for contamination is prompt and adequate, which helped identify the plutonium contamination efficiently.
Nuclear power is very difficult to understand, and the fear of contamination often overshadows the actual science behind it. The public are easily able to understand the dangers of coal, oil, etc due to the highly visible dangers generated by these fuel sources, whereas nuclear dangers are invisible an intangible. Works are inspected thoroughly, but the fear makes it difficult to prove to the public.
Inspecting workers themselves for contamination is an invasive activity that does not allow employees to determine their own course in life. Employees should, rather, have the option to receive testing at their discretion for contamination. Most contamination that is would otherwise go undetected is likely too insignificant to create opportunities for harm to others.
I am sorry to say that I don't have much confidence that those working in Nuclear plants are being given the proper inspections for their safety. I have seen way too much cutting of corners to believe that these plants are taking precautions. Yes, I know in the past they have been called out on not having the proper safety measures and did tighten up the measures, but have they allowed themselves to get laxed over the years since this time. This is what I fear the most.