Different compilers trap different conditions; most compilers have warning level options, GCC specifically has many, but -Wall -Werror will switch on most of the useful ones, and coerce them to errors. Use \W4 \WX for similar protection in VC++.
In GCC You could use -ansi -pedantic, but pedantic is what it says, and will throw up many irrelevant issues and make it hard to use much third party code.
Either way, because compilers catch different errors, or produce different messages for the same error, it is therefore useful to use multiple compilers, not necessarily for deployment, but as a poor-man's static analysis. Another approach for C code is to attempt to compile it as C++; the stronger type checking of C++ generally results in better C code; but be sure that if you want C compilation to work, don't use the C++ compilation exclusively; you are likely to introduce C++ specific features. Again this need not be deployed as C++, but just used as an additional check.
Finally, compilers are generally built with a balance of performance and error checking; to check exhaustively would take time that many developers would not accept. For this reason static analysers exist, for C there is the traditional lint, and the open-source splint. C++ is more complex to statically analyse, and tools are often very expensive. One of the best I have used is QAC++ from Programming Research. I am not aware of any free or open source C++ analysers of any repute.