As far as I know, utilitarians consider that only the consequences should be considered as the calculation of the morality of an action.
Since a mistake and a lie differ only in their intent, are they equivalent according to this philosophy?
Philosophy Stack Exchange is a question and answer site for those interested in the study of the fundamental nature of knowledge, reality, and existence. It only takes a minute to sign up.Sign up to join this community
The evaluation of such a thing looks different under different utilitarian approaches.
Act utilitarianism is a utilitarian theory of ethics which states that a person's act is morally right if and only if it produces the best possible results in that specific situation.
So the first thing that's important to understand is that under this approach an act utilitarian will consider certain lies - those that result in more happiness than not saying the lie - morally a good thing.
An example of this would be:
Thomas has stolen a thousand dollar from his millionaire friend. His friend asks "You are my friend, I trust you 100%, did you steal that money?". Thomas - an act utilitarian - confidently answers he did not, as telling the truth would make both him and his friend unhappy.
This brings us back to your original question where a lie from the perspective of act utilitarianism can thus indeed be morally good or bad in the same way a mistake can be.
Rule utilitarianism is a form of utilitarianism that says an action is right as it conforms to a rule that leads to the greatest good, or that "the rightness or wrongness of a particular action is a function of the correctness of the rule of which it is an instance".
Under this philosophical approach the main question is about how the rules are defined. It's easily conceivable that a rule utilitarian would thus take the approach that "on average" the long term effect of lies makes people unhappy, and thus lies - as a rule - are morally wrong.
Obviously in that case there is a strong distinction between a lie and a mistake as rules are considered an abstraction which ...
Rule utilitarians argue that following rules that tend to lead to the greatest good will have better consequences overall than allowing exceptions to be made in individual instances, even if better consequences can be demonstrated in those instances
Expanding a bit based on the discussion in the comments: weak rule utilitarianism will allow exceptions to be made to the rule in "extreme" cases. E.g. Lies might be always wrong except if it saves someone's life. The opposite of this (strong rule utilitarianism) doesn't allow any exceptions to be made. In either case though there will be a rule involved in the moral evaluation of the case and thus there can be a difference between a mistake and a lie.
And beyond those two there are of course countless of other variants of utilitarianism, so read up on those as well.
The definition of "lie" and "mistake" differ only in their intent, but that does not mean that the set of lies differs from the set of mistakes only in their intent. Given a particular lie, and a particular mistake, it would fallacious to say: "This lie is no worse than this mistake, because the lie differs only in its intent". Lies tend to be worse than mistakes. At the very least, a lie results in a person knowing that they lied, while a mistake does not. Lies are also more likely to result in another person coming to believe that they were lied to.
Furthermore, morality refers to a criterion by which we decide between courses of action. If we know that something is a lie, then it (generally) follows that we should not do it. If we do not know that something is a mistake, then we will not consider the morality of performing mistakes when deciding whether to do it, so our moral judgment of mistakes is irrelevant. And knowing it is a mistake is incoherent: if we know that it is wrong, then it's not a mistake; it's a lie. If a claim is false, then we will consider the claim being false in our decision whether to make the claim only when we know that the claim is false. "Being a mistake" is not an attribute for which it is coherent to include in one's decision-making (although of course "likely to be a mistake" is).
Depends on what you mean by "moral equivalence". If you mean that the consequences are equivalent, then yes, they are the same, but this is independent of utilitarianism. If you mean "both are bad", then they are not equivalent -- to an actor with imperfect information, what in hindsight is shown to be a mistake may have been a perfectly rational, ethical decision when it was made with the information then available to the actor.