"Take Me Home, Country Road" at the beginning of the movie was sung by Olivia Newton-John. The versions which Shizuku sang throughout the movie and at the end were sung by HONNA Youko, the voice actress for Shizuku.
(At 22:56 - 23:20) When Shizuku first follows Muta the cat into Mr.Nishi's antique shop. Just as Shizuku watches Muta enter the shop - we are shown a golden pig statue sitting on the ground being used as a door stop to hold the shop door open, you can see that it's head is angled so that it is pointed/looking to it's right (to the left from our perspective.) But in the next scene we see that the Pig's head is not angled to either side at all - and is instead shown looking straight ahead.