One of the big problems with things like Flash and Java on the web was that they were separate codebases from the browser, but (often) ran inside the browser's

One of the big problems with things like Flash and Java on the web was that they were separate codebases from the browser, but (often) ran inside the browser's memory space, which was kind of a worst-of-both-worlds situation: multiple VMs each with their own individual vulnerabilities, but compromising any one would give you access to all of them. WebAssembly is different because it's built around the high-performance JavaScript VMs that have been developed over the past decade or so. When a browser-maker fixes a security hole in their VM, it's fixed for JavaScript and WebAssembly at the same time, because they're built on the same foundation. So no, you don't have to worry about security as much with WebAssembly - not because of any magical security properties WebAssembly has, but because even though the WebAssembly API is new, the security environment has seen decades of hardening.