HTML rendering is actually pretty consistent among standards compliant browsers (Firefox, Safari, Chrome & Opera). The problem is that the largest browser vendor by marketshare (Microsoft) has a poor history of standards compliance; rather they ignore parts of standards for their own proprietary implementations, which change from version to version.
This has caused Microsoft their current position, where it becomes difficult for new versions of their browser to match the quirks and partial standards compliance of the past versions. It's hard to remove features from a browser when a popular site coded years ago is still using them. In essence, they have painted themselves into a corner.
The problem is not in HTML, the problem is the long term effect of proprietary technology instead of standards compliance. Vendor-owned technologies such as Flash or Silverlight are not the answer, in fact they're characteristic of the problem!