To niggle is to create small but persistent annoyance or discomfort, or to find unimportant faults. It conjugates to niggled, niggles, and niggling. A person can be a niggler. Its adjective form is niggling.
As a noun, a niggle, is a tiny complaint or wince of pain, or something similarly small. It is primarily used in this form outside the United States.
Side note: Another word that shares the same root is niggardly, meaning stingy. But since it sounds so similar to the racial slur, it has slowly become obsolete.