Computing the approximate population of a bloom filter
Yes.  From Wikipedia:

If you have inserted $i$ elements into a filter of size $n$ using $k$ hash functions, the probability that a certain bit is still 0 is 

$$
z = \left(1 - \frac{1}{n}\right)^{ki}
$$

You can measure this probability as the proportion of 0 bits in your filter.  Solving for $i$ gives

$$
i = \frac{\ln(z)}{k\ln\left(1 - \frac{1}{n}\right)}
$$

I have used this in practice, and as long as your filter does not exceed its capacity, the error is generally less than 0.1% for filters up to millions of bits.  As the filter exceeds its capacity, the error of course goes up.