Over Yom Tov I reminded my family of a halacha that will come up once again on Rosh Chodesh when we have the addition of ya'aleh v'yavo in our davening and bentching. If you look in your bentcher, you will see one little difference in the way ya'aleh v'yavo appears there from the way it appears in the siddur: the word melech in ki K-l melech chanun v'rachum atah is in parenthesis. This is based din in O.C. 188:3 The Shulchan Aruch says that when you mention malchus beis David (rachem... al malchus beis David m'shichecha) in the third bracha of bentching you should not mention the malchus of Hashem along side it, e.g. a person should not say malchuscha u'malchus beis David, as if one were to do so it would give the impression that one is equating the malchus of Hashem with another malchus. Adds the Rama, that the same principle holds true at the end of the bracha as well and the word melech should be left out of ya'aleh v'yavo. That being said, the Rama continues and says that he has noticed that the minhag does not follow this recommendation. Achronim (see Taz) try to justify the common practice, but the Aruch haShulchan writes that has noticed that where he lived people do in fact follow the Rama and leave the word melech out. Now that I've made you aware of the issue, you can start leaving it out too : )
One other interesting note on the parsha: Chazal (Sanhedrin 58) darshen from the words "yom v'layla lo yisbosu" that an aku"m who observes a day of shabbos is chayav misa. Achronim say pilpulim to explain how it is that the Avos were able to keep Shabbos (the gemara in Kiddushim tells us that Avraham kept even dinim derabbanan) when technically they might still have had the status of bnei Noach and not been allowed to set aside a day of rest.
Shu"T Binyan Tzion (126) suggests that the key word is "yishbosu." Resting means avoiding hard labor. That is very different that our definition of Shabbos, which is based on the word "melacha," referring specifically to the 39 actions done in the construction of the mishkan. An aku"m who moves a heavy couch between rooms in his house has broken his "shabbos" because he has done hard work, not kept it as a day of "shevisa", but a Jew who does the same action on our Shabbos is not liable because it does not fall into the category of melacha.