It really depends on what you are doing with it.
For things like "I've got this C lib that I want to be able to call from the web" it's probably fine. For things like "I want to write my whole webpage in wasm" it's not ready for that (and, frankly, likely never will be).
It's a matter of finding the right fit.
> If we did decide to go all in on WASM, what sort of gotchas might we be dealing with?
Depends on what you mean by "all in" if you mean, "I want ALL my webapp logic to live in wasm" then the biggest gotcha you'll face is shipping stuff into and out of the VM (including DOM elements) is really painful. IMO, UX continues to best be done with Javascript or compile to javascript langauges (typescript, for example). Using a language like C, C++, or Rust to do UX work will simply not be pleasant, will be hard to hire for, and will complicate a lot of your build system.
Now, if by all in you mean "This logic only lives in this library and we are shipping that out as a WASM module" then I think wasm will work well there. Better, in fact, than other options like kotlin to native or J2CL (IMO).
That said, there are fledgling UX frameworks written entirely for WASM. However, they are all relatively young and AFAIK, not exactly well established.
This becomes an engineering decision and balancing act that I don't think can be 100% answered for your company.