1) Their templating library has a learning curve. It's not quite like svelte, nor like JSX. If you have templates as strings that aren't typechecked, it makes it really hard to work on large code bases where the components are built by someone else and you're the consumer. I remember breaking powerbi.com due to missing > in an angular template that ended up in prod that only triggered for non english customers. It was a hard lesson that day never to touch untyped string based templates ever again. It's so easy to miss something. You want strict compile time checks, not run time.
2) Being dependent on slots. It's not easy to watch for changes in attributes to a slotted child. Yes you can add mutation observers but they aren't cheap either. All sorts of bugs poped up because some code does querySelector(x).setAttribute on a slotted child but the parent doesn't rerender and the UI doesn't look right. We ended up going to json strings inside attributes so components take their inputs via attrs rather than reading slotted children. The other avenue is props (like ionic), but props don't show up in dom explorer, so you have to make the tradeoff.
3) the 3rd big gotcha of web components. Attributes are strings. You have to serialize and deserialize from strings. Sure you can listen to when they change via attributeChangedCallback and get immutability for free because of serialization, but that comes at a perf cost. for deeply nested objects, you have to serialize and deserialize from json.
All in all, I love that Microsoft is doing web components. Webcomponents are part of native dom api with simple lifecycle api. They're neat.