Fellow Scientist and nerd here.
The largest issue with this show is that the characters are unrelateable from my perspective, and therefore probably unbelievable from a non-scientist's perspective. That being said, the mystery surrounding the impending scientific dilemma is just intriguing enough to keep one engaged.
The main contributing factor to the believable/relatable character dilemma is inconsistent dialogue, which seemingly results from the creator's inability to establish the typical characteristics required for properly creating highly intelligent characters and their dialogue. It is impossible to determine whether acting or improper casting is a factor because of the dialogue and character creation issues. Thank God, we don't have to go down any forced-diversity rabbit hole.
As a fellow scientist and nerd, I have many interactions with highly intelligent individuals, and to some degree, all of them are socially awkward, including myself. Socially, the high-intelligence characters seemingly don't have issues interacting with other characters. This is unrealistic. Most scientists are very passionate about their fields and work and typically, science in general. This passion was displayed in the "dinner with parents" scene, which was one of the only relatable scenes, and a great example of good, believable dialogue. This passion needs to be consistent throughout to actually be believable/relatable. This passion definitely needs to be in every dialogue between the highly intelligent characters when conversing science, their work and/or field, and/or the overarching scientific dilemma. Typically scientists, especially the highly intelligent ones, converse and argue about meaning or the deeper understanding of things. This causes them to go off on tangents, which happened with Saul in the "winking universe scene". Again, this type of dialogue needs to be more consistent. The most relatable character is Jack and he isn't a scientist and this likely results more from the items in his room than any of his dialogue.
The Big Bang Theory stands at the opposite end on the spectrum relative to proper dialogue and character creation because those characters fit all of the stereotypes. However, those characters are far more relatable because although it unlikely for highly intelligent individuals or scientists to have every "nerd" characteristic, they will likely have at least a few. This show is is just one example of somewhat proper, relative character creation and dialogue. There are many others, including many Marvel and some DC characters, which makes it mind-boggling that they didn't get it right.