Well no not really. Vulnerabilities exist outside the realms of the language implementations. There are poorly designed protocols and access controls to contend with as well. I'd argue there are a lot more of those classes of problems out there. The ones enabled by programming languages are merely easier to find as you don't have to understand the precise problem domain of the application for each one found.
Maybe every memory access related one. I assume rust still allows you to pass untrusted user input around, for example.
Oh yeah. Cross site scripting and SQL injections are still perfectly easy to write in Rust. You can accept a web POST and pass it directly, unquoted, to a local shell too.
Rust solves every vulnerability ever made
Using a safe language would help even more. Safer than C != Safe.