Which ones and maybe I can comment. I don't think this is true.
> 2) many of the models in economics, while self consistent and plausible, have not been adequately tested with real world data
This is everything that we do. The entire field is all about data and has been for probably 30 years (more actually, but we can point to an improvement in our own standards in the mid-1980's).
> 3) economic models don’t seem to take constraints into account leading to absurd results like infinite growth
A very basic definition of economics in undergrad classes is "the theory of optimizing behavior subject to constraints" so constraints are very much our bread and butter.
Separately I don't think most (or any) macro economists (or growth guys) would say "yeah my model gives great predictions for what the situation will be 1,000 years in the future". Even 50 years in the future is pushing it.
>> at least the way it is popularly understood
This may be your problem. The understanding of the field you find from commenters on this website is a million miles from what it is really about.
1) many of the assumptions in economics are culturally specific
2) many of the models in economics, while self consistent and plausible, have not been adequately tested with real world data
3) economic models don’t seem to take constraints into account leading to absurd results like infinite growth
Within the field, are any of those three seen as important problems? Thank you