EO allow artificial birth control (pill, condoms, vasectomy, tubal ligation) in marriage. They also allow up to two “ecclesiastical divorces”, which means they are allowed to marry up to three times (and some EO Churches allow more than 2 ecclesiastical divorces). ABC and ecclesiastical divorces are not allowed in the CC.
EO say the filioque is a heresy. The CC says the filioque (“and from the Son”) addition to the Latin text of the Creed is perfectly sound theologically, it is not a heresy. EO also reject the Catholic dogmas of Purgatory, the Immaculate Conception of Mary, the Assumption of Mary, as heresies.
As recently as 2006, many Russian priests of the reunified Russian EOC, and many Russian EO believers, regarded the use of the New Calendar (Gregorian Calendar) and the use of pews and musical instruments in other churches (I mean both in the Catholic Churches and in many EO Churches such as the Greek and Antiochian), as heresies. Thus, Russian priests instructed the believers not to present themselves for communion in the New Calendar Churches, and this ban referred not only to the CC, but also to Greek, Antiochian, and other EOC that used the New Calendar, and possibly had pews and musical instruments.
Regarding the role of the Pope, EO theologians maintain that the Pope has fallen into heresy by accepting the filioque, and/or the Pope’s primacy is merely one of honor, but not of jurisdiction. As one poster jokingly put it, the Pope will get the drumstick at the Thanksgiving turkey dinner (after he has repented of his filioque heresy and after he has been subsequently restored to his seat of honor by the EO Churches), but that’s about it. That’s going to be what he will be entitled to, in virtue of his primacy of honor. He is not going to be regarded as infallible in matters of faith and morals, by the EO Churches. The EO Churches are also not going to recognize the Pope’s “immediate and ordinary jurisdiction” in the universal Church, even after he repents of his supposedly heretical views.
Historically, EO Churches also regarded the use of unleavened bread by the Roman CC in the Eucharist as a heretic practice. The shaving of beards by RCC clergy was likewise rejected as unacceptable. These were reasons deemed serious enough, from the side of EOC, to break communion with the RCC. I suspect the Russian EOC still regards these RCC practices (unleavened bread, shaving of beards) as heretic and grave enough to cut off the RCC from communion.
I can’t talk for all EOC, because some of them are agnostic regarding the validity of RC sacraments, and some regarded them as valid at certain times during their history, while others rejected them. E.g. the Russian EOC ruled in the 18th century that the RC baptism and Eucharist are valid, but the present-day Russian EOC regards the RC Eucharist as devoid of grace and mocks it as nothing more than ordinary bread and wine, and also prescribes that converts from Roman Catholicism to Russian EO should be re-baptized, which implicitly means that they do not believe in the effectiveness of RC baptism.
Certain EOC, such as the Russian, regard the Catholic saints, who have been canonized by the CC, such as St. Catherine of Siena, St. Francis of Assisi, and St. Teresa of Avila, as nothing more than self-absorbed and delusional people who should be mocked and made fun of. E.g., the stigmata of St. Francis of Assisi and others were caused by self-hypnosis, and their alleged mystical experiences (apparitions of Jesus Christ, Holy Mary, and angels to these Catholic saints) were either hallucinations of their disbalanced minds, or alternatively came from the devil himself. They have a similarly unflattering opinion about the Marian apparitions approved as trustworthy by the CC, including Lourdes and Fatima - there was nothing supernatural in them, or if there was, that came from the devil, according to Russian EO belief.