Is he to be believed when he promises to impose tariffs on imports from trading partners and to introduce a comprehensive range of protectionist measures? Will he really make good on his promise to scupper the TPPA - a proposal that will be welcome to many, myself included, but that will alarm many others, including John Key.
And what about climate change? Will he really water down the consensus, arrived at after so much effort, on the need for action? And what would that mean for small Pacific nations in particular?
Above all, will a Trump-led America be a reliable ally? Will it stand by its friends if they are threatened by hostile forces? Or does "put America first" mean a withdrawal into isolationism?
Some Trump allies can be heard to say that the stances he has taken on these issues should not be taken too seriously - but in that case, why did he commit to them? If they were merely commitments made for the purposes of the election campaign and can therefore be disregarded, what does that tell us about the reliability of anything that President Trump might say in the future?
Underpinning many of these concerns is perhaps a deeper anxiety. President Obama's dignity, good sense and wide understanding of the world epitomised what many expect from someone who is inevitably and by default recognised as the leader of the free or democratic world. But when we recall the Trump we have come to know - the bigot, the braggart, the self-obsessed chancer, the groper of women, the purveyor of insults - do we see someone who has the moral and intellectual standing to lead us? Does he represent an exemplar of the great virtues of democracy and a symbol of hope to those millions who are denied its advantages? Can he earn the respect that his job demands?
Little wonder, then, that a Trump presidency is viewed with some concern by leaders around the world. That world is now a different place, for good or ill.
John Key, and others similarly placed, must make the best of it. They have no option but to deal constructively, so far as they can, with the new leader of the world's most powerful country - but, in the course of doing so, they might see the need to let him know just what is now required of him by his new responsibilities.
- Bryan Gould is a former British MP and Waikato University Vice-Chancellor