Yes, incompatibilities are almost inevitable. A simple web page is likely to display on all browsers without problems, but the appearance may differ slightly on various browsers. A complex page or a web application may fail on some browsers if it is not properly coded and thoroughly tested.
Macronimous is aware of the problems and codes on websites responsive, which avoids most of them. We use CSS3 style sheets to ensure a robust, maintainable layout, and we test our sites on multiple browsers to be sure they work properly.