I am assuming that it was the builder that claimed the $300 charge - not the attorney. If that is the case, I would first get out my closing paper work and see if there was any signed form that allowed for adjustments between the parties post-closing. I would also look to see if there was anything that obligated the builder to pay 'his portion of' the supplemental tax bill.
Often the purchase and sale agreement states that when you accept the seller's deed the seller will have no further obligations to you, no matter what. However, at closing it is customary to sign an agreement for tax adjustments, so this might 'undo' the purchase agreement language.
In short, the answer to your question is buried in the documents you signed. From what I gather from your question, there was nothing the lender or closing attorney did that was incorrect. It sounds like the builder just didn't get his charges into the closing statement. If that is the case, then perhaps a small claims complaint against the builder is in order.
Most lawyers who handle residential real estate transactions have the parties sign a 'post closing agreement', by which all parties agree to cooperate and correct clerical errors, or incorrect adjustments. You say you received a "supplemental" tax bill, which I interpret to mean that neither side knew about it at the closing. Your closing attorney should be able to help, and if the builder/seller owes a portion of the bill, you could also file a small claims action.
DISCLAIMER This answer is for informational purposes only under the AVVO system, its terms and conditions. It is not intended as specific legal advice regarding your question. The answer could be different if all the facts were known. This answer does not establish an attorney client relationship. I am admitted only in the Commonweath of Massachusetts.