You'll remember that Lothlorien is within a day's march of Moria. You can be sure that Gandalf dropped by for tea with Galadriel before heading towards Fangorn. She probably gave him his cloak then.
Things I noticed that I hadn't before [SPOILERS for Return of the King!]:
- the old whip scars on Gollum's back
- When Gandalf, Aragorn, Logolas and Gimli ride away from Fangorn towards Eodras, they pass a number of villages that are still burning.
- We actually see Osgiliath in FotR, when Gandalf heads towards Gondor to research the ring. Of course, it isn't under attack at the time!
- When half-drowned Aragorn is awakened by Brego, his sword is firmly sheathed. I don't think this is a continuity error, but I do wonder how he avoided dropping it earlier.
- I understand that a missing scene shows Mordor orcs meeting up with the Uruk-Hai. The "meat is back on the menu, boys!" scene makes a bit more sense, now!
- I really want to know where the heck Eowyn is during the battle of Helm's Deep. She isn't shown in the caves with the women and children, and she isn't shown in the battle. I'm wondering if she WAS in the battle, but disguised as a man. In any event, she's nowhere in sight.