The first signal is communication. If you ask practical questions and got vague answers or no answers at all – alert! Red flag! It's a suspicious or clumsy client.
If it's an owner of a business (sometimes you might be working with web-developers or middlemen, and it's all ok as far as they are professionals), check up a website and social network accounts. You would be able to tell how serious a client is.
Almost the same rules that apply to a designer would apply to a client. Check up a website domain name, social networks account names. You shouldn't be however so strict here as a client to a designer should be. A client might be a newbie or just be starting promotion of a business via social media. In this case you might even give an advice to your client.
Next check point, well it may be the first and the last, is a client's readiness to do prepayment. If a client doesn't want to prepay it means he or she either isn't serious about the project, or is trying to deal with multiple designers, or doesn't trust you. In either case you don't need a client like that, it would be wasted time and spoiled nerves. If you are not asking for prepayment – you are not wise. Try to explain a client that you can't afford to dedicate your so valuable time and start a project with no guarantees. Don't be rude however, just explain as it is. A person that is doing a business should understand this.
Even with a prepayment done some clients tend to disappear for a long time or for good. Thus a project is stretching in time or never get finalized. Well with a prepayment you have at least some compensation but the feel of incompleteness stays. Most possibly something big happened in a client's life and a client fails to communicate this, or prepayment money is nothing to a client.
In case it's a client's communication style to disappear for a long time and then continue conversation it should be discussed beforehand. Your responsibility as a designer to walk a client through your process, explain that long intervals between designer – client messages are critical to a project and should be minimized to a day or two. So if a client eventually just disappeared and much work been done already, I would recommend finalizing it, publishing in your portfolio, maybe even making a case study if you are not stressed in time.
Give me some more
There is a type of clients who are never satisfied with a design and always ask for more and more revisions. Remember, it is your responsibility to let know a client how you work before you start a project, explain what your process entails, what you will do and what you won't do.
Your client as a businessman has experience and expertise in his or her area, and you as a designer have expertise in a design area, so your client should trust you what concerns design. It does not mean you are not supposed to do revisions, but it also means you should not turn into a client's tooler. Every time you present a design to a client you explain every single design choice you've made, every time a client asks for a revision he or she gives a proper argumentation of why a design needs revision. Client's feedbacks like 'I just don't like it', 'I don't feel like it' are not acceptable. Design isn't an art and should be judged from its functionality perspective.