Zeus's moral appears to be that one should never defy the will of the gods. In book I, line 55, Zeus mentions that Aigisthos, the murderer of Agamemnon, had been specifically warned by Hermes not to kill Agamemnon, or else Aigisthos himself would be killed by Agamemnon's son.
In line 342 of book I, Athena appears to Telemachus in disguise, and essentially orders him to begin planning how to kill his mother's suitors. Her mention of Agamemnon's death is only in passing—she makes reference to how much glory Agamemnon's son has won by avenging his father, implying that Telemachus would win the same honor for defending his father's household against these abusers.
Nestor cautions Telemachus with the similarities between Agamemnon's situation prior to his death, and Telemachus's own situation. Agamemnon was careful to leave a guard with his wife, but the guard was tricked and abandoned on an island, and then a series of unfortunate delays prolonged Agamemnon's return. Nestor states in line 340 of book III, "don't stay away from home too long or else people will take advantage of your absence, and then your journey will have been for nothing."
Beginning in line 579 of book IV, Menelaus relates having heard of his brother's fate from the god Proteus, and being driven to tears until the god admonishes him that nothing is to be gained by prolonged grieving, and that if he acts quickly he will have time to take revenge instead.