Dirty bomb. Er, no.
The amount of lead necessary to isolate a nuclear core does not encourage any sort of dirt bomb. Even if it blew up in the port, only the ship would be contaminated in a practical manner. To remove said lead to make it worthwhile would cause the death of said terrorists. The amount of explosive necessary to tear the ship apart and cause a real dirt bomb would be put to better use directly. Catch 22.
I hope they do try, and die of digestive and skin systems breakdown (followed by extensive bleeding), which are the first ones to go. Horrible deaths from acute radioactive poisoning FTW.
Submarines are said to use 20% enriched Uranium for propulsion, ground NPPs use 5% at best. CANDU reactors use natural uranium (or something pretty close to it). Not weapons grade, not even close. Which ones will be used? I bet PWRs or the submarine-type ones will be used for ships.
Are they likely to go unstable? It depends on how they are built. RBMK reactors WERE likely to go unstable, and only if badly mishandled they would blow in your face (Chernobyl was this kind, and all safeties were turned off on purpose, and deliberately). No wonder Russia is shutting all RBMKs reactors down in a near future. PWR reactors are not unstable per se, they tend to safely shutdown in LOCA (LOss of Collant Accident) events. Three MIle Island was of this kind, its core melted in a typical LOCA, it vented some gas (controversial?) and they just had to shut it down, as foretold in by-the-book accident event. But that is ground-based NPPs. Both RBMKS and PWRs are lethal if opened while in operation. RBMKs allow the replacement of each nuclear rod, thus allowing the creation of weapons-grade elements, while PWR reactors simply don't allow opening while in operation. I don't know the submarine types to post a remark about them.
Exactly because they are so expensive to build, they are not likely to be operated by untrained personnel. The news mentioned just one private enterprise with such capability, and they are not likely to sell it to operators running on semi-literate skeleton crews. I bet anybody with such capability wouldn´t do it either.
SNAFUS happen, and hard training in combination with an (often) over-engineered machinery leads to safe shutdowns, not catastrophic failures.
My bet relies on PWR reactors, because they operate on 150bar water pressure. (PWR stands for Pressurized Water Reactor). In case they lose the water, (a LOCA, as I said) the reactor shuts down, but the decay heat can still melt it down. Since 150 bar is the rough equivalent of 1500m depth of water, you just have to scuttle the ship in 1-mile deep waters, in a worst case scenario. Ground NPPs rely on double or quadruple-redundancy machinery, with safety on top of safety, and their Operating Handbooks claim 10e-9 to 10 e-12 chance of a really, really, bad event happening. Certainly that is not going to happen on ships.
Again, the type of nuclear reactor is the key factor to determine the safety of the ship, along with the necessary enrichment. The navy can use 20% U235 because the ICBMs on board are equipped with 98% Plutonium warheads, which makes the point moot for ballistic submarines.