"Han har en time på lørdag."

'Appointment' is "aftale" which also means agreement or deal. "En time" means 'an hour' or if you are in school 'one class session' however long that actually is.

I am not sure, but this should only be considered a typo and not a "full-blown" mistake.

"A hour" is not correct. It is "An hour". People in England tend to drop their "H's", i.e. "Otel" instead of "Hotel", and therefor "A hotel" becomes "An otel". If you want to play it safe, always say "an" before words beginning with a vowel, and "a" before words beginning with a consonant. However, there are very few exceptions, "an hour" being one of them.

That would be "han har en tid på lørdag" not "en time" which means 'an hour'.