The USS Puffer [1], Proteus [1], Dace [1], California (twice) [2], Truxton [2], Gurnard (twice) [3], Hawksbill [3], and Abraham Lincoln [3] have all unintentionally leaked nuclear waste into the various bodies of water [1].
The USS Guardfish managed to irradiate it's own crew enough that 4 of them were sent to the hospital, and later managed to contaminate the submarine again while dumping radioactive resin into the wind. The latter form of incident is described as "quite common" [2].
The USS Aspro [2], Sam Houston [3], etc managed to leak radioactive water internally.
The USS Sam Rayburn "is mildly radioactive when it returns from patrol in February 1984. The Navy says this radiation is so mild it cannot be detected by a Geiger counter. " [3] (whatever that means)
(I make no claim that this is a complete list, or even a particularly reliable list since I didn't check my sources sources or anything like that, the point is there have definitely been accidents).
It's true that "there have been no spectacular meltdowns", but you're also talking about operating in an extremely controlled environments of a ship that you control. I don't think the army is going to have as an easy a time at it.
[1] https://en.wikipedia.org/wiki/List_of_military_nuclear_accid...
[2] http://www.chris-winter.com/Digressions/Nuke-Goofs/Refs-70.h...
[3] http://www.chris-winter.com/Digressions/Nuke-Goofs/Refs-80.h...