The most troubling statement Trump has said is his stance on nuclear nonproliferation. Him wanting to expand the number of countries that have nukes is incredibly ignorant.
Then there are the laughable statements such as him saying he would broker peace between Israel and the Palestinians LOL
On the one hand attempting to improve Palestinian/Israeli relationships or even Peace would be a very good thing.
On the other it is a bit like saying "Let's make peace with ISIL/ISIS, what could possible go wrong . . .".
My guess would be that the Palestinians would need some kind of overall leader for the Palestinians, who can unit them, get on with Israel and is a relatively peaceful leader, who wants to and can negotiate a peace deal or at least better relationships.
In practice they (Palestinians) seem to just vote in highly violent and totally untrustworthy, latest version of some terrible terrorist group, such as the PLO, Hamas or similar to ones like Hezbollah etc.
I don't properly understand why, but somehow these communities like the Palestinians seem to end up with highly antagonistic, anti-west leaders.
E.g. Turkey at the moment.
Ironically what is happening to Turkey at the moment, is another GIANT reason, why we still actively need organisations such as Nato. To help us (the west), battle potential future enemies.
What is going to happen if the current migrant crisis (Syria), is made massively worse/bigger, because Turkey goes a similar route. Significant (real) civil war there, is now much closer to becoming a reality.
If anything (in my opinion), the world seems to be a much more dangerous place, now, compared to how it was 20 years ago. Then (1990's), Russia was more a theoretical risk, although Russia did do some bad things even then.
Whereas these days Russia (Crimea/Ukraine), China (significant, forceful military developments in the South China sea, openly threatening the US with nuclear submarine launched weapon, attacks), various Islamic world issues, including ISIS who seem to be actively attacking the West all over the place.
NATO is probably much more important than it was, twenty years ago.
E.g. What if the Turkey/Syria situation gets much worse and out of control. With military action by the west becoming very important. A weakened or even abandoned Nato, could create some simmering nightmare stuff, which just gets worse and worse.
Russia might exploit the worsening situation in Syria/Turkey to their own advantage, and suddenly bring in their fast response soldiers nonsense like in Crimea.
ISIS also seems to exploit weaknesses like Syria and any other countries that are suffering issues.
tl;dr
These times seem to be when we should be strengthening and building up Nato capabilities and international ties.
Not destroying it by an apparently foolish and ill thought out speech, in an attempt to win the US presidency.