Is the activity coefficient always a constant?
In my copy of Atkins Physical Chemistry, 6th edition (it's old!) there is a chart that shows a calculation of the activity and the activity coefficient for an example system (chloroform and acetone). It shows the results using a calculation based on Henry's law (approximating ideal-dilution) and again with one based on Raoult's law (approximating a pure substance). 

In both cases, the activity coefficient is not constant over the range of concentrations.

For some evidence from a less-reputable but more easily accessible source, check out the wikipedia article on activity coefficients:


  $\gamma_B$ is the activity coefficient, which may itself depend on $x_B$


($x_B$ is the mole fraction of the solute).

Now this means that the activity coefficient is not constant for a given substance in a given mixture at all concentrations, but that isn't the same as saying that the definition of activities is not exact - it is exact, because it is defined that way.

In other words,

$$
\mu_i = \mu_i^\ominus + RT\log \gamma_i x_i
$$

is an exact relationship, even though $\gamma_i$ is not constant.