That image is the only one I can find that shows the braiding on a line private. I've have, and can find, hundreds of images that show their coats without, though.
You are correct about the "V" or heringbone pattern button hole lace on the breast of the infantry uniforms. 1814 uniform regulations specified that the button holes be worked straight across for infantry and artillery officers. It was the specialist branches such as general staff and engineeing that had heringbone style lace. All officer's button holes were worked with dark blue silk twist that is often portrayed as black in illustrations, probably so it would stand out better. Enlisted men's uniforms were supposed to be laced on breast and cuffs like the officers but in dark blue cord instead of silk twist, although it may have often been left off to expedite deliveries.
Basically, US uniforms during this period were in a constant state of transition because of challanges of supplying a rapidly expanding army and shortages caused by the trade embargo with Britain. You will find a lot of deviation in surviving uniform articles that in turn results in confusion amongst modern reference sources.
As far as breast and cuff lace on the pictured skin, there isn't any, and that would be historically valid. The shako plate is the old 1812 pattern but many regiments retained their old plates because the new 1813 ones were in short supply. The shako cords should be braided uniformly along their length but that is a pretty insignificant deviation. The pants should be a darker grey but we plan on changing them to white anyway, which would have been worn during the summer. The knapsack straps should be black instead of white. We will change that before final release.
