The media disclose social problems which can monitor and push the government to deal with them

这句话正确无误.
The media 既可以做单数,也可以作复数.例如：
The media almost never do it either.
媒体也几乎从来不考虑通胀影响.
The media loves her not only for her "real" look,but because her story is so inspiring.
媒体爱她,不仅是因为她“真实”的外表,也因为她的故事时如此激动人心.
The media disclose social problems which can monitor and push the government to deal with them