We had the power go out near the beginning of Liturgy one day. It was kinda funny actually, some tried to get it back on (to no success), it wasn't entirely off, but they had to shut off the A/C so the unit wouldn't be ruined.
It actually happened RIGHT at the Great Entrance the exact moment we opened the iconostasis door to begin the procession.
We were wondering how the heck we could get the water heated so it could be poured in with the body & blood, and Father's son did some quick thinking, took the water in the kitchen, and was able to heat it up somehow (I guess their stove isn't electric? not sure how he did it). Other than that, it didn't change the service one bit. The power completely came on after communion.
A couple weeks ago, I was serving with a Priest at the mission that I attend during summers and the Priest actually forgot to open the doors at the beginning of Liturgy, so i kind of had to remind him. We ended up playing it cool and waiting until just before the Little Entrance (since liturgically they would have been closed anyway after the Great Litany) to open them up. Apparently he had forgotten, because they do the opening/closing different at one of the other churches in the area. (I think he said it was the Serbian one)
It was during Holy Week (I think) and Father's other son apparently hadn't had anything to eat/drink for about a day. So we were standing there, Father was standing in the middle of the church (as was required for the service) and his son was standing there by him (to give him the censer at appropriate times). As the choir, we were standing right behind them. All the sudden his son starts to slump, and Father immediately grabbed him and easily set him on the floor (to gasps from everyone). His mother (a doctor) came over and checked him out, he had passed out but was okay, they ended up taking him to the narthex and gave him something to snack on and drink.
It was just something that shocked all of us and almost stopped our hearts, because we weren't obviously expecting it, and it could have been bad had Father not been paying attention to him. (Father apparently saw his eyes roll back and knew he was out before he fell) He ended up being okay, and the service continued. Just a scary moment.
One time one of the cantors uncircumcised Christ instead of making him uncircumscribed...