Issuu.com has a complete or near-complete run of Boxoffice magazine, a publication aimed at movie exhibitors. The site is extremely difficult to search -- the only effective way is through Google, and even that only turns up partial results, and sometimes creates dead links that have to be revived through guesswork -- but at least it's an online resource for information about the movie business through the years. (Registration is free for the site.)
Boxoffice had monthly reviews of short films, including cartoons, though they weren't really "reviews" so much as summaries: the reviewer would recount the whole plot from beginning to end (for the benefit of people who wanted to know whether the films were worth showing in their theatres) and give a rating of "Good" or "Fair" or "Very Good" or "Excellent."
But I did find one item about a short cartoon that went beyond a mere plot synopsis. One of the features in the magazine was "The Exhibitor Has His Say," where owners and operators of movie theatres around the country (often in rural areas) would write in about how a particular movie was doing in their theatres. (I recall that an article on Citizen Kane quoted from this or some similar magazine to show just how badly Kane bombed in rural theatres; anybody outside the urban centres was saying that this was a good picture and their audiences hated it.) And in the issue of May 8, 1954, among all the feature films, I found this blurb:
Duck Amuck (WB) -- Cartoon Short. One of the best comedies we have shown in a long time. A little out of the ordinary in story and very entertaining. The audience liked it. Played Fri., Sat. Weather: Good. -- Paul Ricketts, Charm Theatre, Holyrood, Kas. Small-town and rural patronage.
Chuck Jones made an unusual, experimental film that was a big hit with all audiences, everywhere. That's why Duck Amuck is so great; it's a film that's very self-consciously about the very nature of filmmaking and storytelling, but it doesn't come off as too good or smart to be a regular entertaining cartoon.
Here are two examples of "reviews" from the Shorts-in-Review section:
Bad Luck Blackie
MGM (Cartoon) 7 Mins.
Very good. Blackie, a jet black cat, befriends a white kitten being tormented by a bulldog. Every time the dog crosses Blackie's path, practically everything falls on him out of the sky, from bricks to pianos. When the dog finally removes the spell on him by painting Blackie white, the kitten goes in for black paint, and assorted articles as large as airplanes rain down on the dog. Well drawn and really funny.
Bugs and Thugs
Warner Bros. (Looney Tune) 7 Mins.
Good. Fast-moving, funny film about Bugs Bunny and bank robbers. He gets in the car in which they are making a getaway and is taken for a ride, but as they are about to rub him out, he mimics the voices of approaching cops and they take refuge in a kitchen oven. Then he turns on the gas and ignites it. Real cops then arrive.