Do you have the name of this Viburnum? That may help to establish whether it is normal for that species/cultivar. If you look at the top picture on this page, for example, this viburnum appears to have droopy leaves. I'm wondering if they droop as they age on your plant because the flowers look OK as far as one can tell from the picture:
http://www.st-andrews.ac.uk/~g...
Another option that comes to mind is whether it was watered well before it was planted? If not, even a lot of rain won't necessarily rehydrate the rootball (presumably it was acquired in a pot). Have you noticed whether it is less droopy first thing in the mornings?