Is the event long seen when exploring supposed to keep switching sides? Usually it's on the left like normal, but twice within the past hour or two I've noticed it's switched to the right. Then, when something happens (battle, items, etc) it starts stretching the page. Is that supposed to happen?

Where the log is depends on the size of the island, and the size of the island depends on the level of the pet exploring it. At levels 11, 21, 31, and 41 the size of the island increases, and there isn't enough room for the log to be on the left after the first size increase.