Physics, aside from the major scandals of Ninov and Schon seem to be much cleaner.
Then there is the replication crisis and sokal and its spawn repeatedly showing a lack of rigor and scrutiny in certain fields.
People act shocked when there the public distrusts "science" so much. I don't think its surprising at all. People don't distrust science. They distrust scientists. And there is ample evidence to show they are just as flawed and fallible as anyone else
I will say, however, that we need to be very clear about making a distinction between bad methods and intentional malfeasance. Academic research generally involved a small team of researchers, at best. The code and amount of overall effort involved for what the earlier poster described is extremely intense. For better or worse, code QC simply doesn't exist in most departments for largely financial reasons.
You can generally expect that - most - efforts fall short somewhere, simply because the odds of not making a mistake or two in a 15K+ code base with one or two non-professional programmers are almost nil.
The hope is that another team in the future will tackle a similar task and, in the process, obtain results that are or are not consistent with what were previously published. Thankfully, if the question is interesting or impactful enough, and climate research certainly is, the aggregate body of evidence will eventually force out unintentionally bad research.
Of course, open data and code requirements facilitate this.