Arsenal, Manchester City and Tottenham Hotspur must not slip this week.
What do you mean, how could arsenal and tottenham not slip this week. These two teams will compete tomorrow and one of them must lose or end in a draw. Even Manchester City and Manchester United will also lose points between one of them. so I don't understand what you're saying.
It would make more sense if he mentioned Arsenal and Manchester City should not slip up this week, yes but Tottenham should be excluded.

You are right, the above four teams will probably drop points in their respective match because I think the derby will be very tight. If the match ends in a draw then I don't think all four will benefit, but if Tottenham and Manchester City win then I can expect a change in the table.
this week the big teams will seen the quality of their performance when they meet an equally strong team. The match between arsenal and tottenham will be quite an interesting spectacle tomorrow, partly because they want to maintain their ranking as the leader of the standings this week.
Asenal vs Tottenham, 2-1 to Arsenal win.
Manchester City vs Manchester United. 3-1 to a Manchester City win.
That's the prediction I think at the moment, but we'll see tomorrow between Arsenal vs Tottenham and Manchester City vs Manchester United.