What are two current issues facing Judaism?

Answer 1

Judaism suffers a demographic/integration problem.

1) Many Jews marry non-Jewish partners. This wouldn't be a problem if the non-Jewish partners converted, but many do not. That's not the worst of it. Jewishness is passed down maternally (through the mother), so if a male Jew marries a female gentile, his descendants are not Jews. You can imagine how slowly the Jewish population is growing. It barely keeps even with the Death Rate.

2) Assimilation. Many Jews grow up without a full understanding of their heritage and religion. They lose their religious observance and thus cannot teach their children about Judaism and so on.

Couple the integration problem (marriage, assimilation) with low religious observance and you get a slowly declining population who is unaware of their religion.