Eclipse's compiler has a lot of configurable warnings and errors that other compilers may or may not have. In general the default settings are quite reasonable and you should try to fix them if possible. Many can easily be fixed using the Quick Fix feature: right-click on an error in the Markers (or Problems) view and choose Quick Fix....
Alternatively, you can right-click on the underline (yellow or red) in the code where the error or warning is, and choose Quick Fix....
Not every warning/error has a quick fix, but many do.
If you want to disable a particular warning or error, right-click your project and open the Properties dialog. In there, look under Java Compiler > Errors/Warnings to find all of the configurable ones. You'll have to Enable project specific settings unless you want the same settings to apply to all projects in your workspace.