How others will see it. It's a comedy, of course, and although it isn't much, it is much better it should be. Why the magic more or less works in this particular film is probably due to Costello, and his childish whistles, impersonations, screams, prances, pleas, and other inspired antics.
Perhaps the presence of the spooky monsters gives him a legitimate reason to be frightened. It also creates a measure of suspense, since Abbott is at the peril of one monster or another many times throughout, often blissfully unaware of the trouble he's in.
It further helps that there's a semblance of a plot, although it seems that the monster's brain works well enough already. But he would be more entertaining if he acted like the frantic Lou Costello instead, since as it is Frankenstein is mostly as placid as Abe Lincoln seated at his Memorial in Washington D.C.
How I felt about it. Abbott and Costello Meet Frankenstein works as slapstick. Like a bag of Oreo cookies, it tastes good going down, but there's no nutritional content. It will pass the time agreeably, and for those not introduced to Abbott and Costello, it proves they did more than just the famous "Who's on First?" routine.
Still, the critic in me would prefer it if the story made more sense. How come Chaney allows himself out at night, when he will turn into a Wolfman? How does he know what Count Dracula is up to? Why does Dracula need Frankenstein? To play butler for him, like Lurch in "The Addams Family"? Why does Aubert hang around Count Dracula and Frankenstein, who are both obviously dangerous? If it is for money, how did the Count become sufficiently wealthy? By opening a blood bank?
Yes, that was a cheap shot. Comedies are made to be laughed at (or with). Perhaps it is asking too much for them to fully work as a movie, rather than as simple entertainment. But other screwball comedies have pulled the caper off, e.g. Never Give a Sucker an Even Break (1941).