Have you ever experienced trouble with the Eastern Communion? I have.
No, not the collection of churches themselves, but the actual administration of Communion in the [Byzantine] Eastern Churches can be an occasion for trouble. Much has been made about Communion in the hand in the Roman Church and not without just cause. It subverts the received reverence for the Body of Christ, has lent itself to abuse in the act of giving Holy Communion, and once in a while can permit a Satanist or militant Muslim to acquire a Host with the intention of desecrating the Word Incarnate. The Eastern practice does not lend itself to these exact problems, but that is not to say it is without issue entirely.
The same difficulty with Communion in the Greek rite Churches is that it is almost always administered using a long, ornamented spoon. The Holy Bread must be cut into very small portions in order to remain steadily on the spoon without sliding and the administering cleric must be careful not to impart too much of the Precious Blood other than what has soaked into the Bread.
Unfortunately, the Sacred Species still tends to come off the spoon at least once in a while and end up either on the purificator (Byzantine houseling cloth) or end up directly on the floor. This is further complicated by the fact that children and the elderly often have trouble timing when to open or close their mouths as the spoon approaches. For the split second the Body of Christ is as vulnerable as during His earthly sojourn. At least once every half year some of the Precious Blood ends up on the floor. Thankfully, the Holy Bread more often than not is caught either on the diskos or the purificator. The other week one of our readers attended my parish and found some of the Blood dripping onto the cuff of his shirt.
There is, however, a Byzantine Church that retains ancient practice and has a safer Communion for it. The Melkite Catholic Church retained the pre-Byzantine practice of giving Communion by means of intinction at the hand of the cleric. Practically, this means the deacon holds the chalice next to the priest, who in turn holds the diskos with the Holy Bread. The priest, using his hand and no additional implement, dips the Bread into the chalice and then puts it directly into the communicant's mouth just as would be done in an old rite Roman Mass. The diskos, usually larger than an ordinary Greek one, doubles as a sort of Communion plate, catching any stray liquid or particulars. As the priest directly holds the Body of Christ, the precarious moment when things tend to go wrong is also eliminated.
Communion accidents in the Byzantine rite probably pale in contrast to irreverences in the modern Roman rite, but they remain something avoidable.