Have you tried talking with the attorney in question? Ignored and unpaid bills are a Big Deal for lawyers; we work for money, and we do the work, in many cases, before we see a dime, in good faith that our clients will pay us. We, too, need to pay our rent, feed our children and put gas in our cars, and our fees are how we accomplish this; our time and knowledge are the only things we have to sell. Some of us pursue our fees aggressively, which means, if allowed, collections and judgments against the nonpaying client. Some of us just write the bad debt off, report it to the credit bureaus, and move on. Some of us don't even bother reporting the unpaid fees to the credit bureaus. What may happen depends on the attorney ethics rules in your state, how aggressively your attorney pursues fees, and what fee dispute resolution systems are in place in your state.
Consider speaking with the lawyer about why your are dissatisfied with his/her services. If your lawyer has a partner or a boss (most lawyers who work for firms do), that person should also sit in on the conversation. We can't read minds; your lawyer may not even know that your are dissatisfied with the services provided; once s/he knows that, s/he may adjust his or her bill for you, depending on the policies in effect at his/her firm. Most of us want to satisfy our clients and want to hear about it if the client is dissatisfied with our services. Tell the lawyer (be professional with this; don't scream at the lawyer or lay blame if you want a positive outcome) what you expected that she or he didn't deliver. In the course of that conversation, you might find out what the human being behind the lawyer license had happening during your divorce (personal crises can affect performance on the job for anyone, including a lawyer; maybe your lawyer's kid was very sick or a parent died or ...).
You might also ask another lawyer at another firm whether your expectations for your divorce could have been accomplished. You'll have to pay the other lawyer for the advice. Sometimes clients expect the impossible and there was nothing wrong with the representation except the client's too-high hopes.
I believe Washington has an attorney grievance committee but I, not being admitted in Washington, don't know how to contact that committee. You can find out, though, by calling the clerk's office at the court that granted your divorce and asking for the attorney grievance or malpractice committee's contact info.
I do not know the laws in Washington in regards to debt collection, so I do not know if he is legally obligated to tell you he is sending the bill to collections, but most creditors I have experience both working for, and dealing with on the debtor end in Illinois, notify the debtor when they are about to send a debt to collections. Nothing stops him from reporting the debt to the credit bureau whether it is sent to collections or not.
If you are considering a legal malpractice action, have you considered consulting a legal malpractice attorney to see if you have a case? It is pretty rare that anyone comes out of a divorce feeling satisfied with the end result unless both parties managed to be in agreement before they even hired attorneys for their divorce, but that does not mean malpractice occurred if you are not satisfied. Did the attorney adequately describe to you what typically happens in divorce cases in your locale?
Regardless of whether there is legal malpractice or not, it is typically better in the long run to talk to your creditors, whether they are attorneys or not, about your bill. Ignoring bills is what usually gets people into trouble (ie foreclosures, getting sued for debts, etc). Most creditors are willing to work something out if you make the effort to contact them.