Mr. Smith, like all the characters in the play, is pretty one dimensional. He comes off as a stuffy middle-class Englishman and his character doesn't get much deeper than that. Mr. Smith speaks mostly in clichés and constantly makes dull, superficial observations. For the most part, he doesn't seem to have strong opinions about anything. All in all, Mr. Smith doesn't have too many distinguishing characteristics. Ultimately, he is quite generic and pretty interchangeable with Mr. Martin. This fact is highlighted when at the end of the play he is literally replaced by Mr. Martin.
The one thing that does seem to distinguish Mr. Smith from his counterpart is his love of disagreeing with his wife. It really does seem to be his favorite pastime. Often he seems to contradict her just to be contradictory, rather than because he has a strong opinion about anything. He often even contradicts himself immediately after expressing a certain opinion. The one time he really sticks to his guns is during the great doorbell debate. Mrs. Smith becomes convinced every time the doorbell rings no one is there. Her husband is determined to refute this theory, and argues that, to the contrary, every time the doorbell rings someone is indeed there.
Of course, the very fact that both of the Smiths get so insistent about such a ridiculous disagreement seems to highlight their essential vacuity, or emptiness.
In some ways, though, Mr. Smith's shallowness makes him deep. Let us explain. He can be seen as a parody of your average everyday bourgeois (middle-class) gentleman. You can interpret Mr. Smith's exaggerated generic-ness as a comment on the generic-ness of the middle class everywhere. Beyond that, you can see Mr. Smith as a bit of an everyman, meaning that he represents all of humanity. His meaningless repetitive life, perhaps, represents the Absurdist idea that all of our lives are just as meaningless and repetitious. It seems that, though Mr. Smith's character isn't particularly deep, the philosophies that he represents are about as deep as it gets.