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Nuclear waste leaking into an aquifer or the ocean will not be a local problem.

Not necessarily. Ocean disposal of nuclear waste used to be an option, but was banned in 1993. Studies of disposal sites in use before then seem to indicate that any problems found were very local[0].

[0] https://en.wikipedia.org/wiki/Ocean_disposal_of_radioactive_...

Either it will be local, or it will be dilute enough not to matter.

until it doesn't and it does.

i'm sure that its safe to dump small amounts of radioactive material into the oceans, but if you start to build more reactors and dispose of all the waste into the ocean, the dilution will soon cease to be enough to offset a global ... disaster.

Nope. Unless we start importing uranium from off-planet, there just isn't enough material to make the whole planet significantly radioactive.

What does significantly radioactive mean? If I am a single individual, a single particle of Cesium or whatever could give me cancer. It's not an averages game when you're talking about real lives.

There's natural amounts of radiation that people are exposed to. Taking a commercial airline flight or handling a banana are good comparable measures - if it's less than those, it's not really worth worrying about.

Do you know how much uranium coal plants release into the air?

How concerned are you about cosmic rays?

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