There are protocols that the mobile version of Safari does not support. Java applets (as opposed to Java script) and Flash are the two biggest. When web pages use these, Safari won't work as expected.
Also, sometimes even the code that is supported does not work exactly the same on all browsers. If the web developer did not check for mobile browser and/or mobile Safari compatibility, and tweak it for problems, things can sometimes be glitchy, or not work at all.
Thankfully this second problem is becoming rarer as more and more developers start using tools to check their pages against all the popular browsers, including mobile ones. They are also doing a better job of following the standards. The popularity of third party browsers is to thank for that. When IE was 90% of the user base, developers seldom felt a need to test against anything else.