Steps to reproduce:

with attached project
1. Open attached project "vscode_bug.zip"
2. Open Edit -> Preferences and set Visual Studio Code as external code editor
3. Open "ErrorExample" script

newly created project
1. Create a new project
2. Download and import "Standard Assets" pack from Asset Store (import only scripts)
3. Create a new C# script
4. Open Edit -> Preferences and set Visual Studio Code as external code editor
5. Open new C# script and produce a compiler error

Result: Produced error(y = 0) isn't recognized as an error. Alternatively make another error (eg. "adf - 1;"). You can see that those errors are shown during re-compilation progress, however after script re-compiles errors disappear. (watch attached gif)

Reproduced with: 5.3.6p8, 5.4.2p1, 5.5.0b9