In reply to alps_p:
DMM broke consistently broke 11mm dyneema slings with an overhand knot in them with factor ONE falls (factor 2 breaks dyneema without the knot).
http://dmmclimbing.com/knowledge/how-to-break-nylon-dyneema-slings/
This might not happen if you substitute a suitably squishy human for the steel drop weights, but it would be a pity to find out to the contrary.
Note too, even in the absence of breakage, that dyneema imparts considerably higher loads to the anchor.
Another issue is that some slings have a lot more dyneema than others. Many slings are a hybrid weave of nylon and dyneema. Dyneema is white and doesn't take dyes, so you can eyeball the dyneema content from the "whiteness" of the material.
I'd never heard of a sling used for anchoring breaking in a real climbing situation, but this thread contains two references to such incidents. If anyone has more detailed references, I'd be interested in seeing them.
I think the real point is not, "yer gonna die fer sure if you anchor with slings," but rather, given a spectrum of choices with (at least for skilled practicioners) almost no difference in speed or efficiency, why would one opt for one of the suboptimal alternatives? If you think this way, then you'll always use the climbing rope as the load-bearing connection to a belay anchor.
When it comes to tethers for rappels, the same type of thinking suggests using a nylon sling rather than a dyneema one, or the nylon Sterling Chain Reactor rather than a dyneema blend PAS.