Yes, the FBI often uses questionable tactics in its investigations. Like all other law enforcement agencies, the FBI is allowed to lie to suspects during questioning. Agents routinely will lie to suspects and doing so has been upheld by courts. Agents may also use persuasive interviewing techniques that may border on coercion, leading some innocent people to falsely confess to crimes.
J. Edgar Hoover was very adept at this. His voluminous files on important people contained information on sexual and other improprieties. Such information was rarely made public or used to prosecute. Instead, the implied threat of exposure was used as a political resource. Another example can be seen in the FBI's effort to locate fugitives from the Weather Underground faction of Students for a Democratic Society. A federal agent posing as a radical infiltrated a student milieu thought to be close to this faction. He developed a relationship with a political activist, and she became pregnant. After considerable indecision, and at the urging of the agent, she had an abortion. His efforts did not locate the fugitive. The agent's work then took him elsewhere, and he ended the relationship. The woman apparently never learned of his secret identity and true motives. The situation would have been more complicated had she decided to keep the child or died in childbirth or developed a sexually transmitted disease or become mentally unstable.
I suspect that the FBI probably do sometimes use less than textbook methods to secure closure of a case. The problem is that criminals, especially modern criminals, don't do anything by the book- any book - so the law enforcement agencies are trying to fight with one hand tied behind their backs. Not in every case, but certainly in some, the end has to justify the means.
There's a fine line between the tactics used by the FBI and the true and necessary means of following up on an investigation to help provide safety to those surrounding an incident or for the safety of the general public. Tactics like surveillance and infiltrating personal information should be used if the safety of the public are at risk and the investigation results in a high profile individual.