Bog Brook ends here at its intersection with the Wildcat River. Bog Brook needs to be split here, the upstream portion remains as Bog Brook, the downstream combined flows portion should be re-labeled Wildcat River. Just look at a USGS topo to confirm.

On the Eastern section of the Mahoosuc Trail, the OSM map labels it as Appalachian Trail. It is but the AMC White Mountain Guide description and trail signs use Mahoosuc Trail (AT). At this junction of Mahoosuc and Centennial the AT follows Centennial and then Mahoosuc to the East. Mahoosuc to the West is no longer part of the AT.

As noted just north of this point, the official trail name for the AT here is Mahoosuc Trail, and this holds all the way until the Centennial Trail junction at Mt. Hayes. The AMC White Mountain Guide and trail signs on the trail reflect this typically showing Mahoosuc Trail (AT). I will skip adding notes further East until Mt. Hayes.

This trail is part of the AT, but its official name is the Mahoosuc Trail as described in the AMC White Mountain Guide and the signs on the trail. I don't know if there is an accepted OSM method for handling this but any map label should show the official trail name as well as AT, perhaps Mahoosuc Trail (AT) as it is on trail signs.

This trail is part of the AT, but its official name is Old Speck Trail, as described in the AMC White Mountain Guide and the trail signs on the trail.

The .3 mile stretch of trail running from the AT to Old Speck Mtn is part of the Mahoosuc Trail, not the Grafton Loop Trail. People doing the Grafton Loop will use it, but Grafton Loop the trail starts here at Old Speck Mtn peak. Info from the AMC White Mountain Guide and the trail signs on the trail.

This is not a trail, it is a herd path likely resulting from winter use that tends to repeat and then affects the surface more permanently. It shouldn't show on maps.