Do we take significance of bit into account while calculating bit error rate?
Bit error rate is precisely what it says: the total number of errored bits per unit time. 

Whether the bit happened to be the least significant bit in the coding scheme is of no importance at all in the vast majority of links.

Consider video; if a frame has an erroneous bit, then in some applications I would need to completely discard the frame in some applications if the link had no way of requesting a resend.

Even if the link has a method of requesting the errored frame (such as in ethernet, PCI express and others) errors will effectively reduce the overall throughput of the link.

So - no; the position of the errored bit in the stream is of no consequence.