The Westminster Confession of Faith 25.4 basically deals with is often referred to as “the marks of the true church.” Those “marks” (although the Confession does not use the term there) are the things by which we are to distinguish or recognize whether or not a particular local church is truly a Christian church. (See here.)
Having dealt with the question of the true church in some detail (25.4), the Confession then goes on to speak of the false church:
“The purest churches under heaven are subject both to mixture and error; and some have so degenerated, as to become no churches of Christ, but synagogues of Satan. Nevertheless, there shall be always a church on earth, to worship God according to his will.” (Westminster Confession of Faith 25.5)
The first thing that we should take note of there is that there is no such thing as a perfect church this side of heaven. The Confession plainly states there that “The purest churches under heaven are subject both to mixture and error . . . .” So in seeking to recognize the marks of the true church, we must be careful not to expect to find a perfect church. Even the very best of churches (like the godliest Christians) have faults, failures, shortcomings, and sins.
Mixture and error. That means that we can in this life expect to find false professors and hypocrites in the church. There is really no such thing as a church that always has a perfectly pure membership (i.e. that they are all genuine believers in Christ). And the membership of even the purest of churches consists entirely of sinners. Every last member. Saved sinners? Certainly. Justified sinners? Absolutely? Sanctified (and in the process of being sanctified)? Without a doubt. But sinners nonetheless.
Not only that, but that the best of churches are subject to “mixture and error” means that there is no such thing as a pastor or a church with perfect doctrine in all things (!). As the Apostle Paul says in 1 Corinthians 13:9-12,
“ For we know in part and we prophesy in part,  but when the perfect comes, the partial will pass away.  When I was a child, I spoke like a child, I thought like a child, I reasoned like a child. When I became a man, I gave up childish ways.  For now we see in a mirror dimly, but then face to face. Now I know in part; then I shall know fully, even as I have been fully known.” (ESV)
And so we must learn to tell the difference between, not just a true church and a false church, but also between a flawed church (which is a description of every true church under heaven) and a false church. Imperfection does not a false church make. The flawed church may be far from perfect, but it will still exhibit (even if imperfectly) the true preaching of the Word of God (“the doctrine of the gospel is taught and embraced” – 25.4), the right administration of the sacraments, and the faithful exercise of church discipline (“ordinances administered – 25.4).
Some churches, however, “have so degenerated, as to become no churches of Christ, but synagogues of Satan” (25.5). In other words, sometimes true churches go beyond just being flawed (which all are) to the point of actually becoming false churches. When this happens (to use the words of the Confession), such churches “become no churches of Christ” at all. They may retain the name of “Christian,” but it is really in name only, rather than in any meaningful or true sense.
Sadly, this can be demonstrated over and over again in the history of the church. Churches and entire denominations that once started out so strong, can and do at times “degenerate” even to the point of blatant unbelief and wickedness.
Such things are spoken of (and warned against) in the book of Revelation. In what is often referred to as the seven letters to the seven churches (Revelation chapters 2-3) we read of the words of the Lord Jesus Christ Himself to the church in Ephesus:
“ I know your works, your toil and your patient endurance, and how you cannot bear with those who are evil, but have tested those who call themselves apostles and are not, and found them to be false.  I know you are enduring patiently and bearing up for my name’s sake, and you have not grown weary.  But I have this against you, that you have abandoned the love you had at first.  Remember therefore from where you have fallen; repent, and do the works you did at first. If not, I will come to you and remove your lampstand from its place, unless you repent.” (Revelation 2:2-5, ESV, italics added)
There the Lord warns them that if they do not repent, He would come to them and remove their “lampstand” (v.5). Removing their lampstand is another way of saying that their light has been put out, and that they (the church at Ephesus) are no longer truly a member of Christ’s visible church. (In Matthew Henry’s commentary on this passage, he describes it as Christ unchurching that church!)
Thankfully, this section of the Confession’s chapter on the church ends on a much more encouraging note than that, when it says, “Nevertheless, there shall be always a church on earth, to worship God according to his will.” The church will not fail. Some churches may become false churches, but the Lord Jesus Christ will always have His church on this earth. As He Himself has said, “. . . I will build my church, and the gates of hell shall not prevail against it” (Matthew 16:18, ESV).
Ultimately, the church cannot fail, because the risen, ascended, and reigning Lord Jesus Christ Himself is her owner and her builder. That is why even the very gates of hell can never hope to prevail against it!