Here in the U.S. a hand written will is as valid as any attorney prepared device. Since most of our laws evolved from English Common Law, our will system is pretty standard.
One issue that has been upheld in all of the States, however... a will can not "skip" a generation to avoid paying an estate tax.. That is, a person cannot leave any part of their estate to grandchildren, only to direct descendants, without the "skip" receiver paying a fairly substantial Federal Estate ("death") tax. There, is, at present, a fairly high exemption for the death tax, but our beloved Congress is working feverously to reduce that so as to raise more money to spend.
Most estate laws vary from State to State, but there are a few Federal laws or Regulations that kick in.
By the way, to avoid objections from beneficiaries, the witnesses should (not absolutely required) have their signature attested to by a Notary Public. Here, a Notary Public simply, for a small fee, attests to the observation of the signatures being applied. It's always been found to validate the witnesses in case law suits are brought forth...