I was wondering if the East teaches different severeties of sin as does the Latin Catholic Church -- i.e. mortal sins and venial sins?

I would love to see some discussion on this as well. I know in the past Fr. David Anderson has quoted a passage in Scripture that states that there is a sin which is mortal. I trust him because he's about as Byzantine as one can get. Sadly I haven't been able to recover which passage it was, but I think it is somewhere in the writings of John.

The East has not bothered to categorize sins in this manner, though it acknowledges that some sins are more grave than others. The East tends to look more at the matter of intention, and divides sins into sin proper, which is intentional, and transgressions, which are not. Since both sins and transgressions mar the image and likeness of God within, both require healing and reconciliation to reintegrate the fallen with the Body of Christ, and to advance the person along the path of theosis.

What requirements (if any) are there about confession before taking eucharist? For example in the RC.. mortal sins must be confessed before taking eucharist. Venial sins are forgiven as part of the penetential rite of the Mass.

Requirements vary from jurisdiction to jurisdiction, with some of the Russian Churches being the most rigorous, requiring confession every time before reception. Others vary, according to the attitude of the bishop; frequently it is left to the spiritual father to decide.

The original practice did not require confession before every reception of the Eucharist. Rather, the requirement developed because of infrequent communion (the Eucharist being received explicitly for "the remission of sins", as the communion prayer and various liturgical hymns insist). But, with people receiving less frequently (against the repeated injunctions of the Fathers), and frequently abstaining from Liturgy altogether for long periods, it was felt that more rigorous preparation was required.

As the Orthodox move back towards frequent communion, much depends on the Eucharistic practice not only of the jurisdiction, but of the individual believer. Since most Orthodox parishes are small, priests tend to know the faithful more intimately than in large Latin parishes.

The quote of Sacred Scripture is from 1 John 5:16 - 17
which has been traditionally the proof text for the teaching of mortal and venial sin idea in the Latin Church.
Stephanos I