You're looking for ctags or cscope, the first of which is mentioned in the blog. As for code analysis and warnings, surely that's a property of the compiler being used?
Of course, there are many things for which vim and bash (":%! sort -n" anyone?) are far superior to an IDE. I tend to use both.
It should be pretty simple to add a hook to vim to rebuild the tags whenever you save a buffer, for example. That should take the load off your mind. The issue with IDEs I find is that this stuff is automatic and no way to turn it off, and then I find at the worst time that Visual Studio is crawling to a halt as it runs a load of complex parsing in the background on my 500k lines of C++, just when all I wanted to do was write some code.
Think of it as separation of concerns - you wouldn't write a program where all the code was in one tightly bound monolithic system. Why do so for your tools?
Another not-so-smart feature is auto completion (in C++ at least) and refactoring.
However I can live with these missing features as once you get used to something like Vim or Emacs, its quite frustrating to work on bloated IDE's.
For example, if I Ctrl-] over `open`, and it pops me to the wrong one, I can then type :ts and pick the proper entry (typically with info about the file, type, and container). I can then Ctrl-t back to the previous context as normal.