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 websites in a way, which avoids most of them. We use CSS style sheets to ensure a robust, maintainable layout, and we test our sites on multiple browsers to be sure they work properly.