Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
The "Zidkijah" of this passage is probably the same as "Zadok" Neh 13:13. "Zadok" is expressly called "the scribe," and it was probably as the scribe who drew up the document that "Zidkijah" signed it immediately after Nehemiah.
The names are not personal, but designate families. The seal of the high-priestly house of Seraiah was probably appended either by Ezra or Eliashib, both of whom belonged to it.
Bring ware ... on the sabbath day - Compare Neh 13:16, where this desecration of the Sabbath is shown to have commonly taken place.
Leave the seventh year ... - i. e., "let the land rest in the sabbatical year" (margin reference) and give up the "pledge-taking" Neh 10:2-10.
The third part of a sheckel - This appears to have been the first occasion on which an annual payment toward the maintenance of the temple service and fabric was established. The half-shekel of the Law Exo 30:13 was paid only at the time of a census (which rarely took place), and was thus not a recurring tax. In later times, the annual payment was raised from the third of a shekel to half a shekel Mat 17:24.
No special provision was made by the Law, by David, or by Solomon, for the supply of wood necessary to keep fire ever burning upon the altar. Nehemiah established a system by which the duty of supplying the wood was laid as a burden in turn on the various clans or families, which were regarded as constituting the nation. The lot was used to determine the order in which the several families should perform the duty. A special day (the 14th of the fifth month, according to Josephus) was appointed for the bringing in of the supply; and this day was after a time regarded as a high festival, and called "the feast of the wood-offering."