Question: Should the believing community judge the teachings of its leaders?
Answer: Not only is it permissible, it is our responsibility to do so. Nobody's teachings are above sound judgment - especially influential leaders. Biblical authority and accountability go hand-in-hand (Luke 12:48).
The greater the responsibility one holds, the greater the accountability one has before God and His people (James 3:1).
In the Old Testament, the Israelites were instructed to practice good judgment by inquiring, probing, and thoroughly investigating a teaching or practice (Deut. 13).
In the New Testament, the apostle Paul commands the Thessalonians to test all things (1Thess. 5:21-22) and commends the Bereans for testing his teachings in the light of Scripture (Acts 17:11). Instead of rebuking them, he lauds their character as noble. While our Lord Himself cautioned followers not to judge self-righteously (Matt. 7:1-5), He also counseled them to judge rightly (John 7:24, cf. Matt. 7:15-20).
Furthermore, this responsibility to make right judgments extends to public exposure and correction of false teachings and practices within the church (see Matt. 23; Gal. 2:11-21; 2 Tim. 2:17-18). Christians are frequently uncomfortable with such judgments. They assume that since they are often painful they are also destructive. However, as apologists Bob and Gretchen Passantino explain, "The 'pain' of Biblically-conducted confrontation produces individual growth (1Tim. 4:16), encourages others to Christian maturity (1 Tim. 5:19-20), promotes church strength (Eph. 4:15), and preserves the church's reputation in the world (1 Peter 2:12; [cf. 2 Peter 2:1-2]).