Huge Zits

The other day, I used the "hammer method" to loosen up seized bottom bracket cups on an old steel mountain bike frame and large mounds of rust dust and bits kept coming out of the frame as I was pounding away. It had to have come from inside of the tubes since I cleared out the shell after removing the left BB cup. There are still larger bits in the chain stays that rattle when I flip the frame around.

Should I be worried?

My first thought was to use some kind of rust inhibitor.

What should I do about it?

dabac

Don't worry about it. As iron turns into rust, it expands greatly. I fully expect the bike to remain safe to ride.
And yes, there are bike specific rust inhibitors available, a net search on "frame saver" should yield some useful links. Or you can use linseed oil, or one of the car market rust inhibitors intended to be sprayed into cavities.

xenologer

Maybe save up the rust powder, mix it with aluminum powder in appropriate ratios; make thermite?


Compressed air hose is useful for blasting the annoying rattlly bits out of the frame.

cny-bikeman

The quality and age of the bike would tend to argue against putting a lot of effort into it, as there are likely other problems. It is highly unlikely to fail in any way that would endanger you, but as it is old old if you depend on it for commuting, long distance tours or high speed/hard riding it may be best to just replace it.