Ok, as they are internal, these sort of lawsuits always consider whether the pitch of the stairs is compliant with the current building code.
**** The house was bought brand new and no modifications have been made. Should an inspection be done regarding pitch (the stairs are flat)?
Since you already have carpet and a railing (is the railing on both sides of the stairs?) and if the stairs meet code, then you will not be held liable for any falls as a landlord, as the stairs are in a reasonably safe condition. A landlord is only liable for defects, thus if there is no defect (because the condition is reasonably safe) then there will be no liability.
*There is a railing on the side of the open area. The wall area I believe does not have a railing. Do you know if CA law states that both have to have one?
* How about loose carpet, should I check for that/eg. have an inspection?
To further insulate yourself, you could amend the rental agreement to require that any and all claims, including claims for personal injury related to the property, be brought in arbitration rather than in the courts. This would potentially save you money in a personal injury suit, and arbitrations are friendly forums to businesses.
* We would just notify the tenants of the amendment? Could this look like discrimination as this is being brought up based on seeing their kids who have balance issues falling down the stairs?