> showing code problems without running inspections
You can configure which inspections are run all the time and which are not
> doing Java compilation on save without using Eclipse's own compiler
If you are saving files with Intellij. Configure Intellij to save when focus is lost. I haven't pressed Ctrl-S in 15 years in Intellij. Regarding the automatic compiling whenever you save, like in Eclipse. I am really happy it doesn't do this. Because it means I can work slow compiling projects at all. I can work with refactoring features while my code is in the middle of larger refactoring and it doesn't compile. And so on. But if you prefer Eclipse's workflow, why not use Eclipse?
> doing Java compilation on save without using Eclipse's own compiler If you are saving files with Intellij. Configure Intellij to save when focus is lost. I haven't pressed Ctrl-S in 15 years in Intellij. Regarding the automatic compiling whenever you save, like in Eclipse. I am really happy it doesn't do this. Because it means I can work slow compiling projects at all. I can work with refactoring features while my code is in the middle of larger refactoring and it doesn't compile. And so on. But if you prefer Eclipse's workflow, why not use Eclipse?