Let's compare the S3 opening to the finale closing, shall we?
They're nearly identical with a few very notable differences:
The journal is closed. Her tale is told, this story is done. (It also closes while we watch, driving the point home.)
Her crown is now missing from the pillow*. This is to show how she's now comfortable wearing it all the time, indicating that she's stepped fully into her ruling role in society.
There is more paint spilled on the outside of the tankard that holds her brushes. This is, of course, because she's told a lot more story by the end of the season than the beginning. There's significantly less paint on it in the S1 opening. (And I'm positive the tankard is from the Snuggly Duckling.)
The view is finally pulled back and lit well enough to see what the thing on the far left is: an open birdcage. Rapunzel is finally truly free in the realest sense. She's chosen the life she leads now. None of this is being forced on her before she's ready for it. Interestingly, the birdcage is there in the S1 opening, too, but not only is the shot tighter so most of it is cut off, it's also draped in shadow, making it very unclear what the object is.
But there are some very notable differences between the S1 and S3 opening shots, as well:
The candles in the S1 opening are lit and much higher than the ones in the S3 opening. These are intended to be the same candles, but burned down by S3. This also shows that she's doing her journal entries at the close of the day. But the lighting in the S3 opening implies either dawn or sunset (likely the latter). It's warmer and brighter, more full of possibility and feels less like she's hiding it from the world.
Her paint palette is on the desk instead of her adventure bag which is full of more paint brushes and also coins. She did all of her painting at home, and didn't really have anywhere else to go during S1. She was still doing things the way she'd always been used to doing them.
The wall behind the desk is mostly unpainted in S1 and completely painted in S3. By the end of the series, she'd once again made a home for herself, surrounded by her own art and the stories she had to tell. Similarly, the desk is far less marked up by art supplies in S1 than it is in S3 (just like the brush-holding tankard).
The books are leaning differently, because she took them with her during S2. You can see them in the S2 opening shot on her bed in the caravan.
The little pot in the upper right of the desk has clean, unused paint brushes in it. But in S3, it's full of flowers, instead, because those brushes are all now in use, and stashed in her adventure bag.
There are multiple writing quills on the desk in S1 and none in S3. I feel like this is significant of her always being out and about now. Also, she feel less like she has to "put things in ink," and can instead do her free-flowing lifestyle the way she sees fit.
*Yes, I know that in a previous post I said it was the pillow the wedding rings were carried on, but both of these things can be true at the same time.
