The ULS has the Mister Rogers' Neighborhood Archive; these materials are part of the Elizabeth Nesbitt Collection. Please see the Finding Aid for the Mister Rogers' Neighborhood Archive to understand the scope of the collection. Primarily, the archive includes promotional and production material from the public television series from 1970-1990 (scripts, press kits, publicity photos). For details on accessing the collection, please contact Nesbitt Curator Clare Withers by writing to Ask an Archivist.
Additionally, the Fred Rogers Center at St. Vincent College in Latrobe, Pennsylvania has other materials. You can read more about the holdings in Fred Rogers Archive and may wish also to contact them.
If you are specifically interested in viewing episodes, these are available online via PBS Kids, Amazon Prime Video, and iTunes and may be watched online on Fred Rogers Productions' new website MisterRogers.org.