When do you stop the iterations? The iterations stop, i.e., convergence is achieved, when the data residuals, on average, are at about the same level as the estimated noise. Otherwise you are fitting noise to the model. It is our experience that with proper smoothing no more than 10-30 iterations are needed for convergence.
How do you estimate the average data residual? A quick and dirty method is to simply pick the data and estimate it from your subjective picking intuition. Another quick and dirty way is to say that the pick error is about the T/4where T is the dominant period of the wavelet.
How do you know if you have converged to the correct or unique model? The iterative solution may get stuck in a local minimum, so that the reconstructed model is incorrect even though the traveltime residuals are small. To check for uniqueness you can construct a set of completely different starting models, and see if they all lead to the same final model. If so, then your confidence about arriving at a unique model is increased (but not guaranteed).