Before February 1922, a red star on a budenovka (pointy cloth military helmet) was decorated with 5-6 mm black edging.
The mere idea of sentencing the main character to be "imprisoned" in a hotel for the rest of his life is historically nonsensical: Count Rostov is what the Soviets called a "social parasite," an individual accused of living off the efforts of others, and realistically he would've been sentenced to forced labor, most certainly not to keep living a life of a freeloading.
In the first episode, it's stated that all of Rostov's savings are being repossessed by the state. However, in the next episode, he offers Nina 50 roubles, an huge amount of money in 1922, larger than most salaries.
Count Rostov has pierced ears, which is most unacceptable for a man of his status, or any man at all of the era for that matter.