Your best reference is your local extension office. All provide plant ID/pest and disease diagnosis services for free and will recommend appropriate treament programs. The Internet and specifically GardenWeb forums can help but there is always the potential for misidentification or misdiagnosis when relying solely on photographs. I see it happening constantly.

The plant is Prunus laurocerasus 'Otto Luyken', dwarf cherry or English laurel. Slugs seldom bother any broadleafed evergreens - the leaf tissue is too tough. This type of damage is very common to lots of broadleafed EG's in my area and can be attributed to root weevils. The larvae of root weevils can attach susceptible plant roots but it is the damage of the adult weevils that creates the notching of the foliage. Adult weevils are night feeders so that's why you don't see them. Shot hole disease - exteremly common to 'Otto Luyken' - could also be playing a role but the damage pattern from that is usually a bit different - instead of the edge notching mostly seen in the above photos, distinct holes will develop in the interior of the foliage but if the problem is very pronounced, these lesions can coalesce and could look like the above. I'd approach treatment on both fronts :-) Here is a link that might be useful: root weevils

I can't see what the out-of-focus white spots are, but the shrub is an oleander with what appears to be severe freeze injury. Foliar damage to oleanders is typical in SC. The stems still look green, though. When I lived in SC (Beaufort), I'd recommend that injured oleanders be cut all the way to the ground (ALL the way) in the early spring. These shrubs will grow back better than ever the very first year. If you can take a close-up of those white spots, we'll try to ID the problem for you.

Great, I'm really happy to hear that! This was the first year that it was so tall and covered with berries and it is such a nice shrub. Better than I expected. That is a LOT of Viburnums! There are so many varieties that have something to offer, I can completely understand buying a lot of them. You must have a larger property than my 1/4 acre. :-) I have only six all together and only 4 different varieties. I wish I had room for more. I have two Viburnum carlesii for the fragrance and that is my favorite, but every year it has an issue with the foliage that I've been told may be some insect issue, but I never see an insect. One of them recovers and usually looks okay the rest of the season, but the other one looks bad the rest of the year. I tried cutting that one down to the ground but it did the same thing after it grew back. I'm just glad the other one does okay because I would hate to lose them all together. I have been thinking of trying another one in case the problem was just the source of the last two I bought. Glad your Leatherleaf came back fine for you, appropriate name! I have a 'Red Wings' that I just loved. It was such a quick grower, it amazed me. Unfortunately, all that quick growth made for a lot of breakage. Just as it was reaching the size I liked, we got hit with an October ice storm two years ago and it broke most of the branches off. I did cut that one back to the ground and then this spring a lot of the new branches broke off without even the excuse of snowfall. I haven't decided if I can keep it or not. I cut off what was loose and I've left it to sort itself out. Wondering if after the branches age a little they might get stronger. This winter will be the test of whether it will stand up to all the snowfall we usually get. Well...thanks for the reassurance and sorry I talked your ear off....lol. With that large a collection of Viburnum, have you ever posted photos on the Shrub Forum? Would love to see them.