The three most typical examples: Eusebius is the first author to quote the infamous Testimonium Flavianum (see also Evidence), and he does so without a hint of skepticism (History of the Church, 1.11), and there is strong reason to believe he forged the entire thing (cf. Ken Olson, "Eusebius and the Testimonium Flavianum," The Catholic Biblical Quarterly 61:2, April 1999, pp. 305-22, which also gives other examples of clear and deliberate distortions of his sources); Eusebius is the only author to quote certain imperial letters that he claims were attached to the Apologies of Justin Martyr, but they are obvious forgeries (ibid., 4.9, 4.12-13) and there is reason to believe that the copies attached to the surviving manuscript of Justin were in fact drawn from Eusebius and possibly even written by him; Eusebius quotes a letter written by Jesus, again with total confidence in its authenticity (ibid. 1.13).
Eusebius is also infamous for saying that it was necessary to lie for the cause of Christianity. In his Praeparatio Evangelica 12.31, listing the ideas Plato supposedly got from Moses, he includes the idea:
That it is necessary sometimes to use falsehood as a medicine for those who need such an approach. [As said in Plato's Laws 663e by the Athenian:] 'And even the lawmaker who is of little use, if even this is not as he considered it, and as just now the application of logic held it, if he dared lie to young men for a good reason, then can't he lie? For falsehood is something even more useful than the above, and sometimes even more able to bring it about that everyone willingly keeps to all justice.' [then by Clinias:] 'Truth is beautiful, stranger, and steadfast. But to persuade people of it is not easy.' You would find many things of this sort being used even in the Hebrew scriptures, such as concerning God being jealous or falling asleep or getting angry or being subject to some other human passions, for the benefit of those who need such an approach.
To understand what Eusebius means, it is important to know how the Platonic dialogue he quotes continues (John Burnet's 1903 translation, 663e-664b):
Athenian: Be it so; yet it proved easy to persuade men of the Sidonian fairy-tale, incredible though it was, and of numberless others. Clinias: What tales? Athenian: The tale of the teeth that were sown, and how armed men sprang out of them. Here, indeed, the lawgiver has a notable example of how one can, if he tries, persuade the souls of the young of anything, so that the only question he has to consider in his inventing is what would do most good to the State, if it were believed; and then he must devise all possible means to ensure that the whole of the community constantly, so long as they live, use exactly the same language, so far as possible, about these matters, alike in their songs, their tales, and their discourses. If you, however, think otherwise, I have no objection to your arguing in the opposite sense. Clinias: Neither of us, I think, could possibly argue against your view.
Plato had already had the Athenian argue that justice is the only real road to happiness, and therefore by this argument people can be persuaded to be good. But he then addresses the possibility that the truth will not suffice, or that justice is not in fact the only real road to happiness, by arguing that lying is acceptable, and even more effective in bringing about what is desired, that the people will be good, and thus the government's teachers should employ lies for the benefit of the state.
Regarding Eusebius' use of this and other passages in book 12, Edwin Hamilton Gifford says "In Books X-XII Eusebius argues that the Greeks had borrowed from the older theology and philosophy of the Hebrews, dwelling especially on the supposed dependence of Plato upon Moses." (Introduction, Preparation for the Gospel, 1903). So in a book where Eusebius is proving that the pagans got all their good ideas from the Jews, he lists as one of those good ideas Plato's argument that lying, indeed telling completely false tales, for the benefit of the state is good and even necessary. Eusebius then notes quite casually how the Hebrews did this, telling lies about their God, and he even compares such lies with medicine, a healthy and even necessary thing. Someone who can accept this as a "good idea" worth both taking credit for and following is not the sort of person to be trusted.
Unfortunately, Eusebius is often our only source for much of the early history of Christian texts, and so I am forced to cite him frequently. Even when I appear to cite him confidently, readers must keep in mind that he is not exceptionally trustworthy.