The Ephesian church did have a problem. It was not in holding false teachers at arm's length, but in tending to become lax, to "drift with the tide," as it were, and this made them an easy target for false teachers. In this way, their weakness was, in a way, connected to their strength. They approached matters somewhat lackadaisically when times were fairly good, but when times became bad, they seemed to be able to stand up for the truth.
At certain times, their devotion to God's way left a lot to be desired. Just before the apostle John died in about AD 100, this was very much the case, and he really had to rouse them to get them back. From what we know from church history, by this time the membership of the true church was small and concentrated mostly around John in the church at Ephesus and some of the nearby towns in Asia Minor that he directly pastored.
Jude recognized the beginning of this drifting when he wrote in the mid-60s. All the apostles wrote similar things in their epistles: that the members of the church needed to get on the stick because false doctrines and false teachers were already in evidence among them and beginning to cause problems. If they did not root them out quickly, destruction would follow. The brethren were far too tolerant of divergent beliefs and practices, and Jude, especially, makes this point rather bluntly. He basically yells at them. Those who know Greek intimately say his language is very terse and sharp, and with it he lays in to them for being too tolerant of untruth.
His brother, Jesus, is more circumspect in His wording in Revelation 2:5. To paraphrase, he says, "I would rather that you were strong all the time. You need to go back and do the first works and remain strong so that these false teachers do not get a foothold in the church in the first place."
Richard T. Ritenbaugh