The Times Theatre opened with Waterloo Bridge in 1940 starring Viven Leigh and Robert Taylor. It played opening night of June 29th, as well as the 30th and July 1st. It also showed Of Mice and Men and Buck Benny Rides Again for the remainder of the week. Being a single screen theatre, the Times appears to have consistently shown one film for a few days before switching to the next one. It is notable that the Times and the Strand always showed different films, with the Strand showing titles like Johnny Apollo and a double feature of On Their Own and The Lone Wolf Strikes that same week. Given that both theatres were owned by the same man, BJ Callahan, we can assume they had no competition with each other and were used to show as wide a variety of titles as possible.
The present day Times Theatre and Public House is known for showing much more than films. It often broadcasts live sports, invites live music, and hosts games nights like bingo. While the original theatre didn’t have such a variety of non film events, it still had showings that differed from a classic film. An interesting showing was a film transcription of the play Saturday’s Children by Maxwell Anderson, with which he won a Pulitzer Prize. It played one day only on July 20th at the Times. I couldn't find any other instances of the Times showing news, but an article from August 1st 1940 claimed that the previous Thursday saw the theatre showered in applause when Winston Churchill and British bombers appeared on screen. It was unspecified what broadcast the audience was watching. On May 20th and 21st 1949, the Times was part of a long list of Oregon and Washington theatres that featured the film spin off of the radio show The Life of Riley, along with Old Fashioned Girl as a companion feature.
When the theatre reopened in 2018, it showed films like The Princess Bride, ET, The Rocky Horror Picture Show, and Beetlejuice during its first week, marking its return as a place to see classic beloved films rather than a standard multiplex always showing something new.