First is if you have any criminal history, especially within the last 5 years prior to filing for naturalization. The way the immigration laws are designed, the type of crime, the type of punishment, or the date of the conviction can have dramatic effects on your ability to qualify for naturalization and whether you have temporary bars in place or permanent bars that could make you open to deportation.
Next are applicants with child support or income tax issues. If you have arrearages (debt from non-payment) for either of these obligations, you may be considered ineligible for citizenship. With the right assistance, it is possible to take steps that will correct these problems for immigration purposes and allow someone otherwise ineligible, to qualify and successfully obtain citizenship.
The third scenario that will cause problems for applicants that will prevent them from obtaining citizenship is one or multiple prolonged stays outside the country. This can come in the form of one extended stay outside the U.S. or many trips outside the U.S. since these both violate the terms of legal permanent residency and violate the eligibility requirements of living in the U.S. prior to consideration of citizenship.