This is a, well, disappointing film, which doesn't quite let loose and become a complete satire (a la A Funny Thing Happened on the Way to the Forum). The funny bits seem grafted onto a fairly dull Arabian tale, with half the actors playing it (mostly) straight and the rest (usually) hamming it up. If you are willing to sit through the tedious 1930s-style sword fights, 1940s romance and 1950s-style wrestling matches, you may spy a wildly anachronistic comedy banging on the door asking to be let out and play. Unfortunately, it winds up stranded in the foyer, never quite making it out into the yard for a good romp.
I don't know if Bill Murray is a fan of Dick Shawn, but you can see the sort of hangdog goofiness and wiseguy attitude that Murray epitomized twenty years later. They even physically resemble each other (Shawn has better hair). Unfortunately, the script reins Shawn in at every turn, cramping his style while he squeezes in comic bits. His New York accent alone, juxtaposed against all the flowing robes, colorful turbans and wooden posturing, is good for a chuckle.
There are loads of double entendres, anachronisms and sexual innuendo that will make the adults chuckle, while sailing straight over the kids' heads. Some fabulous character and child actors, such as Stanley Adams and Billy Mumy (incredibly self-possessed in his first role), help carry the load, and, if that isn't enough, there is a talking horse cracking wise (leading the way for the later "incredible Mr. Ed").
I would have liked the film more if the writers had found the courage to discard the straight stuff, add more special effects, and spice up the plot. They could have created a "The Producers"-style romp (where Shawn later showed the comic heights he could reach, given the chance). Unfortunately, the time wasn't ripe, and, but for the snappy "Batman"-style cutaways and a bit of an insouciant attitude, you are left with a film that can't quite break out of its particular time.
Overall, an enjoyable romp that, while dated, can entertain the whole family.