It's fascinating that the board's detractors of 2019 mirror those of 2004. The tuneless criticism always shocked me. "I Hate the Bus" was on repeat on my giant iPod for many months! Even Mr Stopnick and Rose's songs are somewhat catchy, but I suppose it's all a matter of taste.
People also complained that the songs were too short, but this seemed consistent with the theme that things keep changing. The big numbers 1943, Roosevelt Petrucius, I Got Four Kids, and Lots Wife are all plenty lengthy (and very tuneful!).
I honestly don't remember that people thought this story was anti-Semitic during the original run, but Tony Kushner wrote the book, which of course isn't a fool-proof rebuttal.
One criticism with which I somewhat understood in 2004 was that Caroline's disposition was too gloomy. I remember toward the end of the run, the posters changed from Caroline smoking on a bench (the OBC recording artwork) to one with her hands raised and smiling (which I can't seem to find on Google). Yet, why should Caroline be happy? Emmie and Dotty are perfect contrasts, and her situation is pretty awful. Perhaps there could have been a few more moments like "Gonna Pass Me a Law" or the end of Act 1 where she gives her children each a quarter "Open sesame, tell me what see, something silver...", but I never needed much convincing that she cared deeply for her family.