I have have taken a part-time job that pays on the 15th and the 30th; No biggie right. I received my check on the 30th only to learn that this check is for the first through the 15th. I will get my next on 12-15-12 for work from 11-16-12 through 11-30-12. That's a two week lapse in between. Is this correct?

Sure, especially if you are an hourly employee, payroll needs to be processed once your report your time. So its not unusually for there to be a lag of as much as 2-3 weeks depending on the pay cycle. As long as everyone is treated the same, there is nothing wrong with it.