What is the direct significance of the mad dog, the snowman and the tree with the knot hole in "To Kill a Mockingbird"? There are so many...

A symbol is something that means both what it is and more than what it is; symbols function both literally and figuratively at the same time.

1. The mad dog becomes a threat to the children and others on the Finches' street when it nears their home.  So, Atticus shoots it.  However, as a symbol, the dog represents more than what it is.  It represents a true physical threat that can be dealt with in only one quick way.  By contrast, the mob scene of a later chapter in which men converge upon the jailhouse, demanding that Tom Robinson be released to them, so that they may lynch him is not a situation that calls for this one, direct "solution."  Tom is a human being with certain rights, one of which is the right to a fair trial, a right in which Atticus strongly believes.  In shooting the dog, Atticus compromises no principles.  However, were he to release Tom to the mob, he would greatly compromise his priniciples.

2. The snowman that the children build for Miss Maudie is built, as are many a snowman, for the pleasure of its construction and for the pleasure that it provides those who look upon it.  However, the significance of this act is that the Jem and Scout make this delight in snow for the same reasons that Miss Maudie bakes for them:  They wish to manifest their affections for her in a material way.  When Miss Maudie's house burns, for instance, Scout is quick to reassure her that they will rebuild the snowman.

In addition to being a work of their love, the snowman, when first constructed, had to be made of both dirt and snow since there was not enough snow.  The dark soil and the white snow work together, just as black and white must work together in society in order to have successful co-existences.

3.  The tree with a knot hole is like a mailbox for Boo Radley; it is his means of communication with the children through the boundaries of his cofinement.  In it he leaves little gifts for Jem, Scout, and Dill.  When Mr. Radley blocks this hole, he severs communication for Boo with the outside world, a very cruel act on his part, for it again alienates Boo.  Mr. Radley's act is another display of his miscommunication with the world.