Try disabling cookies. This exactly describes the effect, except that it's not mysterious once you're used to it. If something doesn't work, I open it in Chrome (where I have cookies enabled), and it works.
In many cases, I suppose the developer doesn't know about the cookie dependency (because of a framework or some other dependency). In other cases, I guess they don't care. Rarely does the page actually tell you that cookies are required.
Frankly, I don't notify users in any way of a dependency on cookies or JavaScript. If you go disabling features fundamental to the functionality of the web, I expect that you know what you're doing and don't, in fact, expect most of the web to work. The web apps I build simply aren't going to function if you disable JavaScript or cookies.
That is a terribly user-unfriendly design decision because it does not distinguish between failure modes. Maybe your site is broken because I am running noscript or maybe it broken because it is mis-configured or recently hacked or my ISP's proxy is black-holing things or a dozen other things that could go wrong.
The point is that it is relatively trivial for the developer to add automated checks for per-requisites and display warnings for the ones that are missing. It is a lot harder for each user to manually run down through the list of all the things that could go wrong.
If they are missing, tell me your site needs javascript or cookies to operate and I might enable them for your site and give it another shot. But if I just get a catastrophic failure without explanation then I'll probably hit "back" and pick another similar site out of the google search results that brought me there.
Just don't make the warnings into roadblocks. Inform the user and let them decide to proceed or not.
Thanks to recent legislation in Poland webpages should inform user if they are using cookies. Result? Web littered with annoying popups that everybody closes without reading.
Actually, it's possible to implement in it an unobtrusive way that makes users feel more comfortable. The huge popups usually comes from the same websites that do popover ads (that commonly end up invisible and blocking scrolling with adblock) and auto-play videos.
Most of the time it's a small bar on the top or bottom of the screen. Stop whining.
Again, blame the web designers who don't even do enough diligence how others do the same. And demands of proper, obvious labeling is one of the better tools to stop companies from putting useless crap everywhere.
I don't see this. Web is filled with advertising, new laptops are filled with crapware. Labeling didn't do nothing to stop these things. What we get from lawers on the web are idiotic terms and conditions, "I agree" buttons under the wall of text, copyright craziness with idiotic cease and desist, persecution of people publishing secrets or just snooping around. I think if lawyers kept there noses out of the web it would be much safer place.
I agree with you about the design issue. I've had to create one myself (http://tenjin.ie) -- although I think the laws in Ireland are slightly different than elsewhere in the EU.
Regardless of the laws, though, when a site fails to function, it should tell you when cookies are the reason. It's not hard to do.
In many cases, I suppose the developer doesn't know about the cookie dependency (because of a framework or some other dependency). In other cases, I guess they don't care. Rarely does the page actually tell you that cookies are required.