(Obviously, as WASM JIT compilers get more elaborate and it incorporates things like GC'd references, some of the advantages of this design wrt simplicity will disappear, but I anticipate that these kinds of features will mostly not be used in settings like databases).
It does get recompiled to bytecode that runs directly on the processor, so in theory there could be vulnerabilities that come up from that, but I think it’s a pretty well-understood surface area at this point.
Edit: read the first half of my sentence again.
I think that's because the word "binary" has connotations that aren't strictly technically justified. There's no difference between running WASM and running JS (which is usually obfuscated anyway). Both are JITted into machine code, and it's important the JIT is implemented securely. (JIT compilers have been sources of exploits.) The only difference is complexity of the source language, where simpler languages are easier to secure. And WASM is orders of magnitude simpler than JS.
You can already do things like http://www.jsfuck.com/ and even more complex ones, but they would likely have bad performace.
With wasm you could do malware-level obfuscation with less drawbacks.
It is possible that there are a lot of tool to examine JS code for "suspicious code" and that those tools might not work well on WASM.
In practice the WASM interpreter in the browser is a functionality that can be (almost) completely polyfilled.
Personally I would be way more worries about hardware exploits via WebGL.
But it is probably already possible with JSFuck and webworkers.
Flash, Silverlight, Java Applets, and loads more stuff existed while people were still OK serving stuff up without SSL, trying to figure out cookies and generally not putting a lot of thought into cross site scripting attacks. That was a security nightmare and all the obvious things happened. WASM does not seem like a repeat of that. Rather it builds on all the learning we've had since then.
Unfortunately, the design of WASM and common compilers targeting it means that your security is at risk as a user, even though your PC is safe. Applications compiled to WASM have a wide variety of fun security vulnerabilities that have been gone on native targets for decades, which means that if (for example) Gmail moved to WASM, it would now be possible for malicious parties to attack your Gmail tab even though they can't attack your PC. Some examples:
* Address space layout randomization is gone - if an attacker gets a write-anwyhere primitive, it will work 100% of the time
* Function pointers are densely packed - any possible value within the correct range (0 - function count) is a valid function pointer, as long as the signature matches. Even worse than not having ASLR.
* Page protections are gone - all data is mutable, even things that shouldn't be like string constants compiled into the binary
* Zero page accesses don't trap - while compilers go out of their way to try and make reading/writing from null pointers fail in WASM, the actual runtime happily allows you to do it. This makes attacks easier to execute because while stray nulls would kill a native application on dereference, in WASM they will just yield a 0 and execution will often continue.
* Most stuff is static linked - for native applications, it is common (albeit less common now in our modern era of Electron Hell) to pull in services from the OS and its packages, whether it's zlib or https or whatnot. The WASM runtime model generally offers a very limited set of capabilities in comparison, and there's no equivalent way to dynamically link against vendored packages that get security updates automatically. So every application ships its own ICU (for time zone and localization data), ships its own zlib (for compression/decompression), ships its own crypto (because the browser crypto APIs are extremely limited and async-only), etc...
Ultimately WebAssembly runtimes are very secure, but you have to protect everything else from the code you're running, because the code itself can easily be attacked by uncontrolled input.