A few basic things:
Make sure your new employer is comfortable with the arrangement. If the old and new employers are in the same industry, there could be concern about conflict of interest. Depending on how much you trust new employer, you may want to get their OK in writing from an officer or manager.
If you're a contractor with your old company, then you will have to pay both halves of SS and Medicare taxes. Old company should raise your hourly rate to compensate for this.
Old company may not withhold any income taxes from your pay. If so, you'll need to manage things so you don't get hit with underpayment penalties.