will Liverpool make another mistake in the next match?
I think Liverpool will take advantage of this situation to continue to gain points and try to widen the gap with Man City, the opponent they will face after the international break is the promoted club Southampton I don't think Liverpool will make a mistake in this match because Southampton's performance is also very bad playing at home will not have much effect if the opponent is Liverpool. Meanwhile, Man City will face Tottenham if Man City loses again it will make Liverpool 8 points ahead.
With Manchester City currently in poor condition, this is beneficial for Liverpool because they do have the opportunity to get more points and make them far ahead based on their points. With what you said Liverpool will face Southampton of course they have a greater chance of winning, and of course they will make it difficult for Southampton in their match later and make them get points again.
apart from that Manchester City who will compete against Tottenham, maybe they can be made difficult by Tottenham because in their unfavorable condition this makes their performance drop with the four consecutive defeats they experienced this makes them lose points and their top ranking, but even so Guardiola said that he would not back down, he still has confidence to be able to make his team good again.
You are right. Liverpool can use the opportunity that Manchester City is experiencing to secure more points in their matches so they can be able to get so many points that even if Manchester win some goals, they will just be behind them. Liverpool may make it very difficult for Southampton in that match, but we should not conclude about that yet. Let's see what will happen by then, because clubs we think will be easy to win are the ones that make a surprise move against big clubs.