I've always used a Clopper-Pearson interval for binomial confidence intervals, but never questioned why (it's the default in ROOT). I found <a href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval" rel="nofollow">http://en.wikipedia.org/wiki/Binomial_proportion_confidence_...</a> quite useful. Sounds like using Clopper-Pearson is safer than using a Wilson interval .
To be a pedant and assuming your confidence interval is at the 95% confidence level. Taking 73 checks will produce the 95% lower bound 95% of the time if you take any random 73 samples.