BSD and MIT don't mention patents, but have language that can be reasonably interpreted as an implied patent license. You can't use, publish, distribute, and/or sell software and deal with it without restriction if the rightsholder hasn't given you the necessary rights. The necessary rights include copyrights and patent rights. Note that the MIT license doesn't explicitly mention copyright either!
CC0 explicitly says that it doesn't include any patent license, so there is no scope to argue for an implied patent license. The result is that a patent-encumbered software that is otherwise in the public domain per the CC0 device cannot be used, shared, and modified freely. Such terms fail to provide Software Freedom, so CC0 cannot be approved as Open Source. If the CC0 had been silent on the matter of patents or would have at least included a minimal patent license, then CC0-covered software would clearly be Open Source.
The unfortunate result is that there's no good tool to release software into the public domain in a manner that ensures Software Freedom. The CC0 is excellent except for its exclusion of a patent license. While the Unlicense has been legacy-approved by the OSI in the meanwhile, it's a pretty shoddy license, doesn't mention patents, and might not actually work as a public-domain equivalent grant in many jurisdictions.
Note that this isn't a design flaw of the CC0 device. It's great at its job of releasing copyright and related rights into the public domain to the fullest extent possible under applicable law. If a rightsholder also wanted to release their patent rights they could use a separate but similar device. But there's a fundamental difference between copyright and patents: whereas copyright is automatic and must therefore be explicitly released, patents are only granted upon request. If someone goes through the trouble of securing a patent, it's unlikely that they would then want to publicly release all their rights.