I like what you have so far!
To finish it off, I would do a few of the following:
1. I would toss a quilt or down throw or chenille throw on the closest sofa arm to soften that hard edge. A fleece throw would be okay, but will age quicker than the others. Personally, I would try to find (or make) a multicolor item and make sure it has your colors AND includes some blue and/or purple.
2. I like clean simple lines of your windows. I would add something to the walls on either side of the window (maybe both, maybe one, but I am not into symmetry). Multicolor art or sconces or an oval 3-D type shelf to hold a candle....anything that adds some depth and breaks up the round and rectangle theme. I like the round and rectangle, btw, I just would add a third shape. Most decorating principles work best in odd numbers, particularly in threes.
ETA: Depending on how you bring in color and shape elsewhere in the room, this area (window wall) could potentially be a good spot for a few 8x10 or larger portraits. However, I am wondering about the area where the photographer was standing when taking the picture. Maybe that wall (inside the room) would be a better place?
3. One large piece would look fantastic above your sofa. A big oval mirror (horizontal) or a rectangular art piece with organic lines. I would include all your colors in your room (or at least several to tie it in) and I would make sure there were a few cool colors to balance it out. The best decorated rooms tend to have a strong warm or cool color focus and then the accents are in the opposite. For your room, obviously you have a very strong warm color focus (perfect for a living/family room!), so adding a few small accent pieces in cool colors will help finish it off visually and it will help "warm" it up by providing a balance. Adding a bit of deep blue and violet are instantly what I thought of when I saw your picture. I'd also repeat the green you have or break up those three items on the one side table.
4. Do you need lighting for the tasks you do in this room? That is something that popped into my mind right away, also. It looks like you have recessed lights overhead, but what about eye level lighting? A floor lamp with a built-in reading lamp (two lights in one) might work nicely and would also add in some organic lines.
5. While I love the lines of that chair, I wonder what it's function is.... It seems a bit out of place. Right now, the rug color and the chair color tie in nicely. If the rug changes, then I would consider a different item for where the chair is. Actually, I would suggest a big leafy potted tree in that place anyway. It could go behind the chair or in place of the chair.
Have fun with the finishing touches!!!