The small bumps are likely root initials.

Is that something to worry about? The other tomatoes aren't doing that. The stem seems thinner at the base as well. I have it staked up pretty well, so it's not like it needs to hold up it's own weight or anything, but it seems like it's pretty soft there at the base of the stem.

If root initials, nothing to worry about. If that part of the stem were underground, the bumps would develop into roots.

I know this thread is over a year old but I am now growing my own brandywines and 4 of them have the same thing going on that is described above. I planted my seedlings root balls a good 6 to 8 inches down...should I just go ahead and pile more topsoil up the base of the plant where it is thinning and turning brown? The rest of the plant looks great just the 2 to 3 inches at the base getting narrower and harder that looks bad.
Isn't there a disease of the phloem that causes it to collapse and therefore cuts off the sugars transported to the roots...the top of the plant looks good for a while but suddenly dies because the roots (which you can't see) were dying all along? If so maybe I need to rip these out to keep others from getting infected...can't seem to find the answer to this anywhere.