In general, please use the Support link for the developer of the problem app, which can be found on the iTunes page for that app. Most developers (not all though) are very happy to receive problem reports directly from customers, as this helps them more quickly fix bugs and update their apps, and improve the documentation on how to use their app.
Also look within the app for a support link or email address, as many apps have that built in to the app.
For the better developers, contacting them can potentially help improve the app for all their apps current customers.
Of course, final recourse, if the developer is not responsive, or can't fix the problem, is to report your problem to Apple. The contact info for this can be found in the email receipt from Apple iTunes for your purchase, as the "Report a Problem" link. Note, however, that Apple is rarely ever reported have removed merely buggy or ugly apps from their App store, unless the app violates user privacy, decency rules, trademark/IP laws, or worse. You might also want to read Apple's Terms and Conditions of Sale before purchasing any apps.