Several months ago I picked up a 1986 Miyata 710 and started "restoring" it. I had a couple of friends help me take it all apart, re-lube and adjust everything on it. After doing this, I noticed that the crank was loose. We tightened it, and it loosened again. Upon closer inspection, it appears that the problem is with the bottom bracket. If you grab one of the crank arms and shimmy it, the whole thing (crank and bottom bracket) will rock back and forth. We tightened as much as we could (still allowing for it to turn) and it still has some play in it.

Would replacing just the bottom bracket fix this issue or is it possible the crank itself is damaged and the whole thing should be replaced?