If you don't realize that you can call them back you don't deserve the job

You should go over there in person and say that you prefer communicating face-to-face. Tell them you were so super-jazzed about working for them that you messed up on the phone call. Bring cupcakes with frosting to hand out and you'll surely get the job! Good luck!

So snarky today, Alan. ... I like it. :P

Amazing isn't it

Another idea is to offer to work your first week for free. That often overcomes any faux pas you may have committed during the interview process (except for sexual harassment.)

I think calling them back is a terrible idea. I think OP should ignore the obvious, simple solution thereby blowing any chance of getting the job and then write an FML about how he won't be getting that job.

No, wait, I've an even better idea! Just show up for work on Monday morning and act like you were already hired. By the time they figure it out, you'll have proven your worth and they'll keep you on. Aren't you glad we could brainstorm your problem and come up with such a splendid solution?

Just turn up everyday and hang out at their reception. Every time the phone rings, shout "that will be for me" and run for the phone in case it's them calling...

call them back and acknowledge how embarrassing it was to forget to get the two mixed up. Most people won't hold it against you if you're up front about your mistake. Plus, you all can laugh about it later at the interveiw.

what a shame :/ but i guess theyd really appretiate it when you call them back, better than saying nothing :D worth a shot