Does the Almighty's saying, "Most hateful it is with Allah that you say that which you do not do," apply to the owner of an Islamic website who publishes religious topics that he does not entirely apply to himself? And is he accountable for everything published on his site, including errors in verses and hadiths?

A Muslim is commanded to do good and to call others to it. It is a deprivation for a person to command others to do good while neglecting to do it themselves. Whoever commands people to an obligation or forbids them from something unlawful, and then violates it, is blameworthy because their actions contradict their words. They must obligate themselves to what they know of Allah's bounds. Allah says: "O you who have believed, why do you say what you do not do? Great is hatred in the sight of Allah that you say what you do not do" (Quran 61:2-3). And His saying: "Do you order [other] people to righteousness and forget yourselves while you recite the Scripture? Then will you not reason?" (Quran 2:44). This is an encouragement for the Muslim to act upon what they preach, and not a command to abandon inviting to good.