My 14 year old son has generated $700 in earnings from a part time job working as a house and pet sitter while folks are gone out of town. He would like to open a Roth IRA by investing $500 of his earnings in a mutual fund account. Given the fact that he has earned income, is there any reason he could not start a Roth IRA at age 14?

Yes, he can start a Roth IRA at age 14. The key is to have earned income.

Not every custodian is prepared to open Roth accounts for children. You may need to some additional phone calls. Schwab supports kid Roths, I would assume that most mutual fund families also support these Roths.