I know that the beach I'm heading to on Saturday does not allow alcoholic beverages on the beach...we watched a guy get busted last year. (not busted as in arrested, but busted as in, they confiscated his stash). They patrol the beach there.
Not sure about Rehoboth, but I'm thinking they don't allow it either. My friends and I head to OC MD every fall for a weekend, and we take wine on the beach, but that isn't technically allowed either. It's off-season, though, so we've always gotten away with it.