He started off well by killing Jezebel, thereby ridding the country of an evil presence. Where did he go wrong afterward? Did he for instance, adopt her idolatrous practices (or similar ones)?
He went wrong by not turning Israel away from the sins of Jeroboam. These verses sum up Jehu's reign pretty well:
2 Kings 10:30-31 ESV The Lord said to Jehu, “Because you have done well in accomplishing what is right in my eyes and have done to the house of Ahab all I had in mind to do, your descendants will sit on the throne of Israel to the fourth generation.” Yet Jehu was not careful to keep the law of the Lord, the God of Israel, with all his heart. He did not turn away from the sins of Jeroboam, which he had caused Israel to commit.
It's likely Jehu didn't get rid of the remnants of the idols that Jeroboam set up since Jehu "did not turn Israel away from the sins of Jeroboam..." These verses detail what those sins were:
1 Kings 12:28-32 ESV After seeking advice, the king [Jeroboam] made two golden calves. He said to the people, “It is too much for you to go up to Jerusalem. Here are your gods, Israel, who brought you up out of Egypt.” One he set up in Bethel, and the other in Dan. And this thing became a sin; the people came to worship the one at Bethel and went as far as Dan to worship the other. Jeroboam built shrines on high places and appointed priests from all sorts of people, even though they were not Levites.
1 Kings 13:33-34 ESV Even after this, Jeroboam did not change his evil ways, but once more appointed priests for the high places from all sorts of people. Anyone who wanted to become a priest he consecrated for the high places. This was the sin of the house of Jeroboam that led to its downfall and to its destruction from the face of the earth.