Fortunately a bit of "play" in the B key is not as detrimental as other areas of the sax. Excessive "play" or "slop" as techs sometimes call it in the F#, F, G#, Bis keys can make exact regulation difficult or impossible. Play in the spring closed keys, such as the side C, Bb, and palm keys can sometimes cause leaks depending on the spring tension and the depth of the seats in the pads.
In the upper and lower stacks it would be unusual for just one key to wear and become sloppy while the others remain tight. Sometimes a post gets bent outward and creates a gap, but this wouldn't be the cause of your sloppy B since it is in the "middle of the run" on the upper stack.
I would suggest just watching it if the sax is playing well, and the next time you take it in to be serviced, ask your tech to swedge the B key back to a wobble free position.
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