I am curious if Cardinal Ottaviani thought it was invalid or not.  Did he ever comment on that?

I was told the Latin phrase is actually "for the many", and that "the many" means "all" in Latin. Am I mistaken here or what's the story? 

Interestingly, they just brought back the "for many" translation in most of the vernacular languages. 

Right, I think that +Benedict made that change when he introduced his latin-english hybrid new mass.
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But does this fix all the other problems with the consecration formulas, namely 1) the added phrases which imply a narration instead of a sacrificial act by the priest, and 2) the removal of the "mystery of faith" phrase?  Even if a "priest" uses "for many" there are still potential invalidating aspects.
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So, for 40 years, the new mass, when said the in the vernacular, had multiple doubtfully valid problems.  How many "masses" were affected from 1969 til 2008ish?  Here's the calculation:
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40+ years, times 52 sundays, times 1 billion catholics = approx. 2 QUADrillion (that's a 1,000 trillion) catholic were deprived of a valid mass.  Even if you assume that only half used "for all", it's still 1 quadrillion.  That's a lot of invalid masses, which have absolutely no graces.  0%.  zilch.
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It's insanity that people keep defending the novus ordo.

He's referring to the Greek where many with the article, so "THE many", means "the multitudes", which could be rendered as "all".  Perhaps you've heard the expression "hoi polloi".  Only problem for this theory?  The Greek version given in the Gospel of St. Mark LACKS the article "the" and simply says "many".  Many in Greek without the article can never mean anything other than many.  Lots of these glib little answers from Novus Ordo-ites who haven't actually done the research.

Another answer was the claim that semitic languages lacked a separate words for "all" and "many" ... which has been long debunked as a lie.  Not to mention, you're claiming that the Holy Spirit in rendering the Greek (it is the Greek text that the Church holds to be inspired), happened to chose the wrong possible translation of the semitic, an error with Bugnini and company were able to correct the Holy Spirit about ... nearly 2000 years after Our Lord said the words.

So, since both of these reasons are demonstrably garbage, WHY did they mess with this?  Was it just to make the Church seem more welcoming to all of humanity or was it to deliberately invalidate the Mass ... just to make sure?

Right, if you look closely enough at the NOM, the Anaphora I is essentially the Roman Tridentine Canon.  I actually believe that the Novus Ordo Mass, taken in and of itself, using Anaphora I, is more likely than not valid.

I think that the Rite of Ordination is positively doubtful due to the removal of a word that had been declared to be part of the essential word.  It's debatable whether it changed the meaning enough, but there's enough there to cause doubt.

I don't see how the Rite of Episcopal Consecration could be valid.  Father Cekada's study took it apart.  It was lifted from a rite that most closely resembles the installation of a Patriarch (who was already a bishop) and failed to specify the power of order being granted.