A Minor if he is too young to walk with his father/ride his father's shoulders: Chagigah 2a, 6a
A Minor who has reached the Age of Education: Chagigah 4a
A Mother brings her under-age child to Jerusalem, which is as far as her own requirement of holiday ascension goes, and then the father brings him to the Temple: Chagigah 6a
A Minor who is Blind/Lame, but may eventually be healed, and therefore should perhaps be brought as Education: Chagigah 6a
Men who would be shunned from the group due to their odor: Gatherer of Dog Excrement, Copper Miner, Tanner: Chagigah 4a, 7a-b
The Mitzvah does not apply to one who does not own land: Pesachim 8b
An individual with a prosthetic leg: Chagigah 3a, 4a, Yevamot 103a
