> Nowadays, it looks like this:
http://imgur.com/a/Z7IXuWhat browser is that in? It looks like a weird bug is showing there, potentially an exploitable one since some of that looks like garbage pixel data, like it's reading from invalid memory. That seems to be the issue here, not that web content isn't like the "old days" when it always worked but was sometimes wrong.
Speaking of which, there never were any "old days" that I can remember. Often sites only worked in IE, not just rendered properly but also only worked. You couldn't enter data into forms, or couldn't get them to submit properly. The web wasn't just a little incorrectly rendered in the IE days, it was totally broken on many sites.