In my home office, there are parts of the floor that seem to be chipped off.
Their pointy edges keep catching my socks when I walk by.
How would you solve this problem?
Ideally the solution would not just solve the sock-snagging problem but also improve the appearance of those parts of the floor.
I have access to a Dremel and could try sanding them down, but I don't know what would happen and what I'd be risking.
These are "shakes" - this is where the lumber separates along the growth rings.
Fill the cracks with glue (PVA / polyurethane / epoxy / cyanoacrylate) then place cling wrap over them and weigh it down with a large bag full of sand (or something else soft and heavy) while the glue sets. Scrape off any excess glue, fill any voids with filler... and now the bad news. This is caused by moisture. You probably need to sand and re-finish the floor.
When facing a similar issue in my home office (but with smaller bits of damage) I found a good color-matched wood filler, and applied it according to the package instructions. It has held up well, and is visible but not objectionable. That would be my first step in this case, as it's easy to undo or redo if you continue to have issues.
See the other answer as well from Jasen for what you should do to prevent this happening again.
