The most common mistake I am seeing is when employers classify workers inappropriately as independent contractors and issue the worker a 1099-misc when the workers should really be treated as employees and receive W2s subjecting wages to employment tax. For more on this topic check out these posts ...

http://johnrdundon.com/employee-vs-independent-contractor-business-owners-tips/

http://johnrdundon.com/employer-misclassification-of-workers/

In my experience, one of the most common mistakes I've seen in payroll accounting is in the area of state and Federal unemployment tax. Either the computer systems aren't set up correctly or the bookkeeper/payroll clerk doesn't know the law, but many companies fail to stop paying the tax on wages above the maximum wage base subject to the tax.

With regard to your second question, I would agree with John. Misclassification of workers to avoid payroll taxes is a high audit area for IRS.