I wouldn't say he's "gone wrong with the rebuild" just yet.
But he has made some bad moves, and between the Walman trade and missing out on most FAs, his offseason so far has been quite poor. Holl was a bad signing. Copp was a bad signing. Petry was a bad trade. Fabbri's renewed contract is/was bad. The Husso experiment has been a failure.
Hope is not lost and there is still lots of time for things to go right. But in the last 1-2 years, it's fair to begin to question Yzerman's vision and plan, or at least the execution of said plan.
As far as good moves:
He has drafted very well in the first round every year. Seider was a great pick. Raymond was a great pick. Ed looks like a great pick. Kasper looks like a good pick. Danielson looks like a good pick. Cossa looks like a good/great pick.
A big part of Holland's failure near the end of his tenure in Detroit was messing up the 2016/2017/2018 1st round picks in Cholowski/Ras/Zadina, and Yzerman has been significantly better in that respect. It's easy to hit on top 10 picks, but it's not easy to hit on top 10 picks 5 years in a row. As long as Danielson and Kasper do well, Yzerman has done that. That deserves commendation.
Beyond that, DeBrincat was a good trade, as far as capitalizing on something that fell into our laps.
I don't really think he's made many commendable moves beyond that. Squeezed out some decent value for Mantha, I guess. Compher was an average signing. Kane, I'm still not the biggest fan of, but it's acceptable. That's really all.