Since it was previously established that Pete is 42 and the writers took 3 years off of Claudia's age now making her 19, Pete is actually old enough to be her father.
When Pete walks into the medical MJ shop he puts his arms on the counter but in the next scene his is walking to the counter again.
Pete says that he remembers thinking it was weird that Peterulz 1 through 22 were taken, but passwords don't work that way. There is nothing preventing users from having duplicate passwords: however, usernames do have to be unique.