Broaden your client base
Perhaps the biggest mistake that any newly self-employed person can make is to get tied to one or two clients only.
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.