"The play was so popular that the theater was almost full."
Translation:Lo spettacolo era talmente popolare che il teatro era quasi pieno.
"cosi'" can be and adverb or a conjunction. When it is an adverb it can have two meanings. It can mean:
(in) this way, like this, like that "Ho scritto cosi' (I wrote like that)" "Non ho detto cosi' (I didn't say that)"
so, so much "E' cosi' gentile (he is so kind)" In this case "cosi'", "talmente" and "tanto" are interchangeable. The DL sentence can be written as "Lo spettacolo era cosi'/talmente/tanto popolare che il teatro era quasi pieno"
Is there anything wrong with "Lo show ha stato così popolare che il teatro ha stato quasi pieno."?
Yes, you have to use "è stato", not "ha stato". I think that Duo can accept this. Try the next time.