Specifically the Mass? Well, I think in and of itself it presents a *potential* danger in that it is not specific about certain dogmatic teachings, most specifically the propitiatory sacrifice of the Mass. It does not outright deny it, so it is not a danger in terms of putting forth heresy, but if your priest is not on the ball about preaching about that, then I am unsure how you would ever absorb that idea. It is scandalous if you are familiar with the TLM and see what has been cut out.
Overall, I think the whole Novus Ordo liturgy and Church are problematic for several reasons. Perhaps the most serious problem, because it touches everything, is the idea that Tradition doesn't, at the end of the day, actually matter. The Pope matters. We can be cheerleaders for JP2 when he defended moral teachings, and now we can be cheerleaders for Francis for undermining moral teachings because he's so merciful. It does not matter what the Church said or did in the year 50, 550, 1550 or 1950, because we have Paul VI/John Paul II/Benedict XVI/Francis and the "god of surprises."
Flowing from that cavalier attitude with Tradition is the distinct impression that "the Church can't really take all of this seriously can it?" If you can change the Mass, all the sacraments, smash altars, throw out religious habits, discourage devotions, etc., none of this can be serious. So I'll believe and do what I want, and there's certainly no reason to invite my non-Catholic friends to the Faith - they're fine where they are!