A Joke and A Serious Question

First the Joke:

Back in the 30s Sheinar Shendle was a new immigrant to the US from her shtetl in Poland. She quickly found a neighborhood fool of landsmen and found a rabbi to consult for her shailas. She had one peculiarity - every Friday morning she took her chicken to the rabbi to check that it was kosher. Week after week she came, the rabbi looked, and pronounced it kosher. Finally, after many months, the rabbi asked her "Why are you bringing these chickens to me to check every week? You should only come if you see something that makes you doubt it is kosher." Sheinar Shedle replied "I knew it! But the other ladies in the community insisted that A&P grocery store chickens were treif!"

The serious question:

If I bring home a chicken today from a shochet, rather than buying it at the store, is there any kind of inspection that can be done to reveal that the chicken is actually treif? Obviously we can't review the knife, or whether the shochet said the blessing, but what can be done? On the one hand, there are lots of stories about women taking their chicken to a rabbi when they aren't sure it is kosher. On the other hand, once the feathers are off and the internal organs removed, what is left to inspect?