Reading this verse reminds me of one of the first Christian books I ever read. It said something that, at the time, seemed strange to me. It advised the reader to pray and ask God if there was anything they are doing wrong at that moment. I remember thinking how could I be possibly be doing anything wrong right now? I'm sat at a desk reading a book.
As a more mature believer, I understand that we're always in a state of sin. We do, say, and even think sinful thoughts on a regular basis. God is an honest critic. He knows exactly what our weaknesses are. Our fears, our goals, our achievements, our failures, our past, present, and even our future. That puts Him in a perfect position to point us in the right direction. He can tell us "you need to improve here". Sometimes, He can do this instantly. "Hey God, am I doing anything wrong?" "Yes. Do you think I'm pleased with that naughty tab you have open right now?" Other times, He uses something, or someone, to point it out.
By far the best way to find out if you're offending God is to read the Scriptures and compare your life to them. It is often said that expecting God to answer your prayer while your Bible is closed is like expecting to receive a text while your phone is switched off. This is certainly true. In Romans 7:7b, Paul says "...I had not known sin, but by the law: for I had not known lust, except the law had said, Thou shalt not covet."
As a new believer, I wasn't exactly familiar with the Bible. I knew the Gospel. Jesus died so that I could be forgiven for my sin. But I had no idea what sin was, at least not in detail. The most I had was a slight familiarity with the 10 commandments. By contrast, I knew the ways of the world very well. A lot of the things I just assumed God would be ok with, because everyone around me was ok with, are actually an abomination to Him. But I did something the world doesn't: I studied His word with a faithful heart, the result being a gradual, and of course ongoing reformation in my heart so that I may be gradually conformed to the image of His Son.
As human beings, sin will always plague our lives. But as an old enemy once told me, "it's ok to not be ok, but it's not ok to stay that way". If we are truly saved, we need to throw off our old sinful nature and put on the righteousness of Christ. But before a problem can be dealt with, it must be identified. Thus, let us say wit the Psalmist, "search me, O God", and let Him direct us in His ways.