The white bits you have seen in your probiotic are quite common. Some of the bacteria in it are anaerobic – this means they normally live in an oxygen free environment. When the liquid is exposed to the air, during the bottling process and obviously when you open it, these bacteria act to create the right environment for themselves – i.e. they try to “protect” themselves from the air by forming a skin of sorts.
The sediment is evidence that the bacteria are alive and active. It is perfectly safe to drink the product, white sediment and all, and the sediment will not affect its effectiveness.