Titus - General
Titus 1:2 - Paul says that God, like George Washington, cannot tell a lie. But he managed to do so in 1 Kings 22:22-23 and Jeremiah 20:7.
Titus 1:6-7 - A bishop should have only one wife. Apparently, it's OK for laymen to have several.
Titus 2:9 - Paul tells slaves to obey their masters and "to please them well in all things ... showing all good fidelity." But Jesus (Mt.4:10, 23:10) said that his followers should have no masters.
Titus 2:11 - "The grace of God ... hath appeared to all men." At the time this statement was written, only a very small minority had seen or heard about Jesus. And still today there are those who have never heard his name.
Titus 3:9 - Paul instructs us to "avoid ... genealogies." Like Gen.10, 1 Chr.1-9, and Lk.3?
Titus 3:10-11 - Heretics are to be rejected since they are subverted, sinners, and condemned by God. The Jehovah's Witnesses [and other Christian groups] follow this teaching by disfellowshipping those who refuse to accept the Governing Bodies teachings. (The NWT translates 3:10 in this way: "As for a man that promotes a sect...." But don't all JW’s belong to and promote a sect?)
Philemon - General
Philemon 12 - Paul returns the runaway slave, Onesimus, to his "rightful owner", Philemon, asking him to receive him just as though he were Paul's very "own bowels." This was, of course, a great opportunity for Paul (and God) to condemn slavery, if he (and God) had anything against it, that is. But he doesn't. Instead he returns the slave to his owner without a word against the institution of slavery.