The danger is most acute if you've been moved sideways off the payroll and then rehired to do a version of your old job as a 'consultant'. Leaving aside the tax issues (ie are you really self-employed?), the danger to the long-term viability of your new business venture is insidious.
At the beginning it all feels great: you're doing a job you know how to do, maybe even working with the same co-workers and customers as before. You're probably feeling better off financially as you're billing more in fees than you were taking home in salary. But because you're an ex-employee working (hard) in such a familiar environment, it can be easy to forget that the single most important aspect of successful self-employment is broadening your client base.
You can't ever afford to forget that fundamental, usually unspoken, change in your status: to sever all ties with you, all the client (aka 'your ex-employer') needs to do is to stop returning your calls.
Much is written about marketing and self-promotion and so on but let's cut to the chase: your goal must be to cultivate as many viable clients as you can. It's only with a range of income streams that you can start to feel any sense of that stability that is a necessary precursor to business success.