1. Should the question be “is entertainment okay?”. Perhaps is having “fun” okay? Are you arguing the relative merits of watching a baseball game versus learning gemara, or perhaps as opposed to going to a concert, or perhaps compared to reading a book (as opposed to learning a sefer).
2. Certain sports have specific halachic issues (swiming and “beach volleyball” come to mind very easily). While the ancient Roman “sports” were clearly avoadah zarah (yes, gladiators were a human sacrifice – not an athletic contest), one might find certain aspects of modern sports questionable as well (boxing, dog fighting, etc.).
3. If a sport is permissable to participate in, is it also permissable to watch?