Should Nick trust Gatsby?

Nick should not trust Gatsby. There are several reasons for Nick not to trust Gatsby. These develop and emerge throughout the novel.

The first is simply that Gatsby hides his past. If someone keeps secrets, there are always questions about what happened/what he did in the past.

Next, Gatsby has an affair with a married woman. Regardless of how much he loves or desires Daisy, he's still involved in breaking an oath and a social code.

Gatsby deals with criminals, suggesting that what he is hiding is illegal too.

I would suggest that Gatsby's incredibly expensive parties are also a reason to not trust him. He is not hosting a lot of friends. He's not even holding these parties because he's running for office, and needs the approval of the guests. He just has some deep and badly defined need to be approved of. That suggests there is some gap deep in his character.