Shit HTML structure: no headings, junk links, adds that have 50 elements only containing a "."
Slow websites / jank doesn't go nice with voiceover so all javascript that runs after the initial set up should take 16 ms to run (enough for 60 frames per second)
Unlabelled buttons and checkboxes,
Links with only an image or icon to indicate what it's for.

This is too general of a question I think, plus it has some personal preference.

Check out $1org particularly the most recent survey and the WCAG 2.1 guidelines. Trying to meet at least Level A and preferably Level AA would be good.

The thing that frustrates me the most is when websites and web apps don't follow WCAG level aa criteria and when the devs don't do any usability testing with differently-abled stakeholders, plus when they don't create things inclusively or incorporate empathetic design into their sites.

I use zoom for websurfing. By zoom, I mean zooming the browser and lowering the screen resolution.

Too many website assume we are using a 4K monitor and don’t let us zoom out the picture so we can see all of it. Imgur is one such website.

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As a young, post web 2.0 screen reader user (i.e. despite not having anything to relate this to) I think most of the modern web is way too bloated. Sure, javascript can and is used very elegantly to achieve very useful things, but with all of the analytics and tracking these days, everything become^so a crawl. It doesn't matter if I'm using my acer c720 chrome book running a very minimal arch linux installation or my 2010 mac pro running any of the 3 operating systems on it, loading youtube.com takes an age, not to mention all the images it has to download that I can't see. Light web pages are always faster and easier to access.

I think people get heading levels wrong way too often. Screen reader users use headings to navigate through the sections of the page, so if the levels are wrong, it becomes a pain, depending on how the user is navigating. Even if you don't want the styling of an h3, at least set your h4 to have an aria-level of 3.

Overall the thing that puts me off visiting a site is when parts of the page change without user input. This is very confusing to screen readers and their users and often breaks navigation from and to other parts of the page. A good example of this is badly designed dialogs asking, for example, about cookie usage. Depending on the platform the user is browsing on, it is very often possible to read and navigate through objects on the page not only covered, but restricted in interaction by the dialog. as you can imagine, add into the mix the very likely possibility that the screen reader user isn't even notified that a popup has appeared and it can be a very confusing and frustrating experience, one that could be solved or at least improved with little use of the aria-hidden attribute.

Most of my web frustrations are common internet annoyances. Although there's one that has to do with accessibility.
I can't stand CAPTCHAs that don't have an audio equivalent. At this point, it's pretty rare that I run into that, but it's extremely annoying when I do! Also, the sites that try to inflate page views by using slideshows as lists, and putting 5 of 25 items on the first page.

My 2 biggest pet peeves:

1. Pop-ups. Seriously... there are times I have to take deep breaths to not throw my laptop computer against a wall because I'm so angered by this fucking pop-ups everywhere. I use inverted colors on my computer because I can't see text anymore otherwise. Pop-ups are usually dark, which means they are extremely bright (white) on my screen. Since they come without any warning, I suddenly get blinded by this horrible, bright light. What's worse is that the x-button or the "no, thanks"-button are always super tiny, so I have to squint and harm my eyes by looking for those damned buttons for several minutes. It's pure torture and just so frustrating. I'm not interested in whatever BS that website wants to sell me and after giving me such an unpleasant experience, I'm even less inclined to give a damn. Sometimes pop-ups are so bad that I can't handle the situation. I have waisted too much time in my life dealing with this stuff. This is why I've made a rule for myself. If I can't find the x-button within 10 seconds, that's it. I'm leaving and never visiting your website ever again. Still, I wish web designer could finally stop annoying VI/blind people with pop-ups. By the way: yes, I do have a pop-up blocker but many types of pop-ups show up anyway.

2. Websites that fall apart when you zoom in. I don't get this. How hard is it for website developers to check whether their sites collapse when zooming in before they open them up for the masses. I mean, just take a MacBook and zoom in with the pinch-motion. It takes a few seconds. If everything on your website overlaps and your screen looks horribly chaotic now, maybe redesign it a bit. There are websites I am forced to leave again for the simple reason that I can't zoom in and if I don't zoom in it's too small for me to see. By the way: a great example of this would be reddit. I am exclusively using old reddit because new reddit is total crap. If you zoom in on new reddit, your screen becomes a total mess and the surfing experience very unpleasant.