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It'd affect the matter distribution and density of the universe immensely.
The intergalactic medium is about 1 nuclear mass per cubic metre, and this would be increasing that by 238.
The universe overall has a density of 10^-26 grams per cubic centimetre, and the added uranium would have a density of 3.95×10^?22 grams per cubic centimetre. So over the course of billions of years, the universe would collapse.
Interstellar gas has a density of 200 to 50,000 atomic masses per cubic metre in the bulk of the galactic plane, with tiny spots with a density of 100,000 to 10^9 atomic masses per cubic metre.
Overall, the density of interstellar gas is only significantly increased in particularly low density regions.
The amount of radiation you'd be exposed to would increase with time, as the light from new radiation sources reaches you. It increases asymptotically; half life would not cause it to eventually start dropping, as although nearby radiation sources would gradually cool down, when the light of distant radiation sources reaches you it's from when the plutonium was still fresh.
I'm not sure how to calculate the radiation dosage you'd get from this.
