I don't think 'mistake' is the exact word to use. Tarot read 'in the moment' may tend to cause a few blank spots, a backout or two, or some other such thing that once we said 'what came to mind' we start to have second thoughts about it.
There is nothing wrong with this; we are human - humans make mistakes.
If you are asking "I meant to say 'Summer' and I said 'Winter' by accident" there is nothing wrong. The earth will not fall from it's sphere; 21-year old scotch will not turn to iced tea.
If you are asking " I told them to stick with their lover, but now I see it is an abusive relationship and they should not stay together," You have a moral dilemma. I am guessing that this 'realisation' comes during the reading, not hours later after the reading is over? If you are doing longer eadings, such as 10-card spreads, you can get different information (think of it as progressive information) at the start and finish of a reading. If later information reveals an unsettling truth, there is nothing wrong with saying to the querent 'These later cards are telling me something I think you should know .....' . What you say to a client is not written in stone, nor will saying something in a reading actually cause that event to happen. Being truthful to the querent where you may say "At the beginning the cards were telling me _____ but now that the final cards have come into being I see that ________" is a better thing to do.
As far as 'pulling the wrong card' - many of us don't think that this can happen. Tarot will get you the answer that is needed. Even if you carefully shuffled the deck and accidentally dropped it on the floor - the card you pick up first will have the answer you need. If you don't believe this you probably don't have enough reading experience or possibly trust in your abilities. The best thing to do is keep reading cards - for yourself, for family, for complete strangers.
Even the experienced among us 'stumble' at times; but we know we have to keep moving forward, and I hope you will continue to do so, also.