I dont know if this is a bug or not, but when ableton is synched to the beat buddy (beat buddy sets the tempo) the tempo fluctuates constantly. it is very minor, but perhaps is something. when the beat buddy tempo reads 100 for instance, the ableton tempo will be 100.01 or 100.02. sometimes its 99.98 or 99.99. Just wanted to call this to your attention.
This may be caused by a MIDI cable, for example, if it is long enough.
Also, 0.02 BPM is actually a very small value to worry about. If it also actually fluctuates (and is not always 100.02), then there is no need to worry, as I believe overall BPM will average out to 100.
Did you probably notice any other issues that might get affected by this?