In his 1961 review of Disney's Babes in Toyland, John L. Scott writes:
This "Babes" represents an expensive translation of Victor Herbert's operetta with typical Disney effects It's considerably more showy than either Herberts stage original or the first film version done in the middle 30s; and older patrons may re sent a loss of quaintness ana a surplus of fantasy-whimsy.
How would Scott have seen the [1934 adaptation](https://en.m.wikipedia.org/wiki/Babes_in_Toyland_(1934_film))? How would critics of this era in general amass knowledge about the content of films from previous generations? Nowadays a critic has access to a huge proportion of twentieth century cinema through archive prints, DVD, streaming services, digital piracy, and even VHS.
Wikipedia mentions that Babes in Toyland was broadcast in the holiday period on local TV stations across America, but presumably most three decade-old films were not regularly screened on television. Would a film this old still be doing the rounds as part of repertory programming in theatres? Or would critics just build up their own personal memories of films over the decades and draw on those, with little opportunity to ever re-watch most of them?
A film critic would definitely be aware of the "classics" that would show at festivals, although the 1930s Babes in Toyland doesn't quite count for that status. However, the movie did get re-released as March of the Wooden Soldiers in 1948 and then put into TV syndication after; you can see this 1953 issue of Billboard explaining that Peerless Television sold their film to "seven new markets, bring total of sales on the picture 21" including Philadelphia, Houston, and KTLA in Los Angeles, where your critic definitely could have seen the film on television.
In general, by the 1960s, the pipeline had opened up anyway for films -- there was a fight over residuals that finally got resolved, so while a very specific film might still be hard to see without a very expensive rental, that wasn't the case for something that could run as a holiday special.
I have more detail about this in a prior answer. A big film critic in LA would have more access than the theoretical average person on the street I was writing about (both in terms of proximity to film studios and ability to wrangle actual equipment).
Private projections were also a thing before DVDs and VHS. I studied film in college and we had a small projection room to watch old films in, equipped with many projectors for many film formats, including 35mm. I’m sure a critic or film writer in the 60s would have access to that equipment to watch films as well, as physical copies shown in theatres in the thirties were very much still around in the sixties (since we still have some today). Also, film studies departments were already a thing in the sixties (the first film school in the US opened in 1929), so private film viewing for professional or research purposes was definitely possible, no repertoire cinema needed.
And in the process of making a movie, you need to watch it on a big screen for testing and editing (directors watched dailies while they were still shooting and big studios loved screen tests back then too), so those facilities were certainly available from the moment films started being made.
In conclusion, that critic could have watched Ben-Hur as he was typing his review.