I've searched the AppleOne web site and I've found some positions that interest me. However, the positions are posted from other AppleOne offices. Is it alright to apply for these positions even though it's not the AppleOne office that I visited? I don't want to cause any problems that my hinder my job hunt.
You can apply to jobs posted by other offices. The person staffing the job will look to the people they know first, so if you are interested in jobs at other offices, you should probably consider registering with that office. Finding a job is about personal relationships, so developing additional relationships can only help you in your search.