Is it permissible to continue treatment with a male dentist who is trustworthy and skilled, especially since female alternatives were not up to the required standard, knowing that he did not uncover any 'awrah and is nearly sixty years old?

If refraining from treating your ailment would result in harm, and it is not for beautification purposes, and no female doctor is available to treat your condition, then it is permissible to seek treatment from a male doctor under certain conditions: that you are accompanied by your husband or one of your mahrams to avoid unlawful seclusion (khalwa), that the doctor is trustworthy and reliable, and that he only examines the area needing treatment.