1) A lot of SPA websites nowadays break my browser's Back button. I understand that this is "easy" to fix with push state/history APIs, etc. But it never used to be this way. Now you have to do all kinds of special stuff just to get the basic functionality of your web browser back.
2) SPA apps almost always have to be specially routed at the webserver level to the index.html. Again, it never used to be this way. Without any special server-side routing I now have to visit the main page and then follow a series of SPA links to get to the page I want. I can't just go directly there anymore because most likely the CDN or webserver will return a 404. Again, it never used to be this way. Fundamental aspects of the web have been broken.
What are some other annoyances?
So I'll change it up and say: the lack of keyboard-driven functionality taken into account. There are many people (me included) that would love to almost never touch their mouse. Emacs? Never use it. Terminal? Never use it. Browser? There are very few pages I can operate without using it.
Thankfully, groups like DuckDuckGo have thought about it. I can navigate DDG without touching my mouse, which I utterly appreciate, and is the reason it's my primary search engine. Not just the privacy aspect.
2. Not well documentation in web apps.
3. Files that are blank or just say that you need to enable JavaScripts, without any documentation or alternate protocols links.
4. Overuse of CSS and JavaScripts. (Better using plain HTML and then user can use their own options instead.)
5. Bad design of the standard specifications, and bad design of too complicated web browsers, without enough user controls.
6. Overly complicated API designs.
7. Videos even though I would want to read it as a text instead.