You can also have the exact opposite problem with RAII, where a resource survives the end of a transaction, because there is still a live reference to it hidden away somewhere (say, due to some debugging code holding on to it). This is a classical liveness vs. safety dualism. "Something good will eventually happen" and "nothing bad will ever happen" are promises whose solutions are often in conflict with one another.…
Oddly, Rust's ownership system really does solve these problems, and Non-lexical lifetimes should eliminate accidental scope-broadening. Unless you are doing some mega-schenanigans, an e.g. MutexGuard gets released precisely when you think. Your point about this being difficult to solve in the general case is true, it's just worth pointing out Rust intends to do that hard thing anyway.
No. Rust's ownership problem solves it for trivial cases, at the cost of making it hard to do other things (such as sharing references past the lifetime of the owner without resorting to Rc or Arc, at which point you don't really have lifetime guarantees anymore).
The essential limitation of Rust is that (without resorting to Rc and Arc, which would put you back to square one) it is conceptually limited to the equivalent of reference counting with a maximum reference count of 1. In order to make this work, Rust needs move semantics and the ability to prove that an alias has a lifetime that is a subset of the lifetime of the original object) and may even sometimes have to copy objects, because it can never actually increase the (purely fictitious) reference count after object creation.
This inherent limitation makes a lot of things hard (or at least hard to do without copying or explicit reference counting). Structural sharing in general, hash consing, persistent data structures, global and shared caches, cyclic data structures, and so forth.
In short, you have the problem with shared references less, because Rust makes it hard to share data in the first place, for better or worse. (Again, unless you resort to reference counting, and then you get the issue back in full force.)