Right now we're focused on the first release of OpenTelemetry, which will include distributed traces and metrics. Many users and contributors have asked for logging support, and this was already a big discussion topic in the pre-merger OpenCensus and OpenTracing communities - I'd expect us to start focusing on this after the release later this year. There have also been some early conversations around support for an error first-class signal type (there was a recent GitHub issue, though now I can't find it), however to my knowledge we haven't yet started any error-related specs or design discussions.
You can certainly add error-related annotations to traces, however these will typically be sampled.
Error information is a bit different than general logging - stacktraces, annotation of exceptions with case-specific information, matching that data with debug symbols, etc. It would be interesting to see the ability to enrich standard logging with custom-shaped data, without sampling, in a standardized way.
You can certainly add error-related annotations to traces, however these will typically be sampled.