As of TypeScript 2.6 (released on Oct 31, 2017), now there is a way to ignore all errors from a specific line using // @ts-ignore comments before the target line.
The mentioned documentation is succinct enough, but to recap:
// @ts-ignore
const s : string = false
disables error reporting for this line.
However, this should only be used as a last resort when fixing the error or using hacks like (x as any) is much more trouble than losing all type checking for a line.
As for specifying certain errors, the current (mid-2018) state is discussed here, in Design Meeting Notes (2/16/2018) and further comments, which is basically
“no conclusion yet“
and strong opposition to introducing this fine tuning.