It looks like a user/users can register multiple accounts using the same email address.

Basically when user registration is restricted (to be verified by admin) and a user registers, the account is inactive. While inactive, the same email address can be used multiple times and multiple accounts can be created using the same email address. Should this happen?

Email is unique, cannot be used on multiple registrations.
Admin does not verify user registrations.
I was not able to reproduce, got error:
"The specified e-mail is already in use"

I meant, user has to confirm the registration. But if he doesn't, he can use the email again.

So the flow is: user registers - confirmation sent - user doesn't click the link - user registers again using the same email - new account created - new email sent - and so on.

Email is unique, cannot be used on multiple registrations.
Admin does not verify user registrations.
I was not able to reproduce, got error:
"The specified e-mail is already in use"

Still valid, email is unique no matter what is account status..

Do you use the same name for Name and User Name fields? If so, try different.

Ok, it was my bad. It looks like I'm blind and the email was similar to the previous one (one letter was different, the user misspelled the name). So it works all as it should, sorry for your trouble. 

@morfik
No prob