Many databases have filters or ways to limit searching by date, document type, etc. If you need film reviews from a certain time period, look for the date settings in the database and limit it to "reviews".
InfoTrac Newsstand provides access to more than 2,300 major U.S. regional, national, and local newspapers thousands of newspapers from across the world. ProQuest Historical Newspapers database has full-text articles from a variety of U.S. newspapers including the New York Times from 1851-2011. Entertainment Industry Magazine Archive covers primary sources from the 1880 to 2000.
The Film Literature Index covers 1976-2001, and while it does not have full-text articles, this will help with finding citations for historic articles. Randall Library may carry them in print, or using Interlibrary Loan will be available for those resources not in the collection.
For a full list of newspaper databases available, check the Newspaper Resources page.
A website that has reviews and other useful resources is CineFiles.