Note: due to the design of PM, the search is done client-side rather than server-side. It's not an excuse but at the very least, full-text search is harder.
I can't even think of any? But also search isn't a core feature for the vast majority of sites. Something can be easy and still break if nobody cares very much.
Edit: Actually I can think of search breaking on one site that was notoriously badly run and had 0 to 1 part-time devs. That's not a flattering comparison.
Edit 2: So could the people that disagree name some notable sites with broken search? I feel like if I don't understand what "XYZ" stands for it's probably not something I should be blamed for...
Then there's MDN - a documentation site, whose 2nd most important function should be search. Yet, despite DuckDuckGo (a general-purpose search engine!) consistently finding the exact results I want, MDN's built-in search often misses even titles that are searched for verbatim.
If it weren't almost 2am and I weren't running almost entirely on caffeine, I'd probably be able to think of a few more.
When you can download a freeware tool that will find any file in the system instantly after maybe a minute of indexing you know the file search is not the problem here.
Just a month ago the only reason I could start a recently installed MS Office package on Windows 10 was its tendency to list newly installed programs first in the start menu. It did not show up anywhere else, could not be found by the search and Word could not even be set as default program for a file because the OS didn't seem to know of its existence.
I know for a fact, Gmail on my phone doesn't have the ~15 years of email in my account downloaded. I bet that would take significantly longer to download than the actual search would would take to perform.
If the things to be searched aren't already on the client, a client side search doesn't seem too useful to me, regardless of how much compute power you have.