Thanks, everyone, for all the information.
According to his website, Jussi Halla-aho was a researcher and instructor (Fi. tuntiopettaja) of Old Church Slavonic in the department of Slavic and Baltic Languages at the University of Helsinki from 2000 to 2006.
According to encyclopedia articles, the Church Slavonic used in services today is a later development from Old Church Slavonic. Whether this should be understood as implying as big a difference as that between, say, the English of Chaucer and that of Tolkien or as small as that between the language of Dickens and that of J.K. Rowling, I can't say since I don't know either form of Slavonic.