Is there a saying like 'those who find faults with other people tend to be blind to their own faults'?

There's

That's the pot calling the kettle black,

...which indicates that a pot hanging over the fire will be just as black (that is, in the same state) as a kettle. There are a number of variations on that saying; it's so well-known that generally it suffices simply to mention "pot" and "kettle" in the same sentence.

And the Bible has something to say on it, eg in Matthew 7.

“Do not judge, or you too will be judged. For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.
      “Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye? How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye? You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye.” [NIV]

Again, the last sentence is so well-known that simply reminding someone [using the King James Version] to take the beam out of their own eye will often be enough.

Matthew 7:3

And why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye?

(King James version)

Other versions

The standard variant is:

Remember that when you point a finger at someone, there are three pointing back at you.

Google threw this one up:

Fools can find fault, but they can't act anymore wisely. - Langbien

This is a classic, in English and other languages alike:

We see the straw in the eyes of others and we do not see the beam in ours.

Matthew 7:3 is the inspiration.