Practically zero hardware acceleration. A single HD webm already pushes an i5 2500k to ~10% CPU usage. I fear what would happen on a page full of auto-playing webm videos.
Webm, like h264, is a video codec. The browsers aren't designed to have several dozens of them playing at the same time on a single page.
WebM is just a container. The codec,
VP8, is 6 years old and was the last version of the TrueMotion codec lineage by On2 Technologies before they were purchased by Google, who open-sourced the codec.
The problem is the lack of hardware decoding. Decoding modern video is very taxing, but we hardly notice it because nearly everything uses h264, which has ubiquitous hardware acceleration support. Disable hardware acceleration and h264 becomes as CPU-intensive as WebM, if not more.
VP8 completely failed on getting hardware support from hardware vendors. On PC, only some Intel GPUs actually offer hardware support while on mobile only a few Android devices do it.
It seems Google is working hard to fix this with VP9, which is the rival to h265 in becoming the "4k generation" codec. However, this means we'll probably need new hardware to play accelerated VP9 (NVidia and AMD GPUs might get shader/compute-based decoding via drivers, but mobile devices and intel IGPs need new revisions.)