A fine cast and director Leo McCarey's expert sense of the absurd make this a very amusing classic comedy. It is a good example of what master craftsmen can do to turn a thin and deliberately implausible plot into a fun movie.
The actual story is pretty simple, serving only as a setup for a lot of pleasant nonsense - Cary Grant and Irene Dunne play a couple who get divorced, and then make each other jealous when they pursue other relationships. Both leads are excellent, and they are helped by a good supporting cast. Ralph Bellamy is well-cast as a bumpkin who starts a relationship with Dunne, and Alexander D'Arcy has some very funny moments with Grant, as Dunne's voice teacher who provokes Grant to fits of jealousy. Not an awful lot really happens, but there are a lot of zany moments.
If you enjoy these 30's 'screwball comedies', "The Awful Truth" is one of the best ones, and you almost certainly won't be disappointed with it.