Acts 24:14 (Amplified Bible)
14But this I confess to you, however, that in accordance with the Way [of the Lord], which they call a [heretical, division-producing] sect, I worship (serve) the God of our fathers, still persuaded of the truth of and believing in and placing full confidence in everything laid down in the Law [of Moses] or written in the prophets;
Paul's own admission, during his trial at Jerusalem before Felix.
Matt. 17:3 And behold, Moses and Elijah appeared to them, talking with Him.
Moses represented the Law. Elijah represented the Prophets.
Matt. 5:17 "Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill.
They found their fulfillment in John the baptist (Luke 16:16) and Jesus' coming.
But they're not abolished.
Luke 16:17-18 "But it is easier for heaven and earth to pass away than for one stroke of a letter of the Law to fail.
Earlier we see:
"No servant can serve two masters; for either he will hate the one and love the other, or else he will be devoted to one and despise the other You cannot serve God and wealth." 14Now the Pharisees, who were lovers of money, were listening to all these things and were scoffing at Him.
15And He said to them, "You are those who justify yourselves in the sight of men, but God knows your hearts; for that which is highly esteemed among men is detestable in the sight of God.
And in context,
Everyone who divorces his wife and marries another commits adultery, and he who marries one who is divorced from a husband commits adultery.
Jesus is saying that the Pharisees were abandoning God for money and that they will be judged by the law or something like that.
Anyways...
I take another position:
Then again,
Matt. 17:3 and 5:17 are what Paul is referring to.
The NASB renders Acts 24:14 in this manner:
"But this I admit to you, that according to the Way which they call a sect I do serve the God of our fathers, believing everything that is in accordance with the Law and that is written in the Prophets;
In context,
Acts 24:15 having a hope in God, which these men cherish themselves, that there shall certainly be a resurrection of both the righteous and the wicked.
Basically, Paul is
affirming his belief in the resurrection, the primary driving force of a believer (1 Cor. 15:17) and what distinguishes him from other religious men. The passage does not mean that Paul kept the law.